Divergence

Results for NTCIR10-FT-4

Query

Original Query

NTCIR10-FT-4 Full Text Query Divergence \prod _{{N=1}}^{{\infty}}(1+Z/N) N = 1 ( 1 + Z / N ) Z C superscript subscript product N 1 1 Z N Z C diverges diverge The “open problem” at could use a hint.

Compiled by FSE

Token-Filter

  • TeXFilter:[+, N x 2, (, ), /, infty, 1 x 2, \ x 2, _, ^, =, prod, Z]
  • Presentation-MathML:[1 x 2, C, +, ∞, ∏, N x 2, /, ∈, =, Z x 2]

MathML-Filter

mrow[msubsup[mo[∏];mrow[mi[N];mo[=];mn[1]];mi[∞]];mfenced[mrow[mn[1];mo[+];mrow[mi[Z];mo[/];mi[N]]]]];mrow[mi[Z];mo[∈];mi[C]] apply[apply[csymbol[superscript];apply[csymbol[subscript];csymbol[product];apply[eq;ci[N];cn[1]]];infinity];apply[plus;cn[1];apply[divide;ci[Z];ci[N]]]];apply[in;ci[Z];ci[C]]

Word filter

Keywords:[diverges, diverge] Rendered Presentation-MathML: N=1(1+Z/N)ZC

Results

Summary

Reviewer score 2

  • Items reviewd: 40
  • Accumulated score: -119806693
  • Formulasearchengine found: 13

Reviewer score 0

  • Items reviewd: 60
  • Accumulated score: -119844047
  • Formulasearchengine found: 12
.
+++o
200000+0000
5000-2000000131225
<50000274875
04060100
50000000:0 200000:0 10000:1 5000:1

Short result list

Detailed results for reviewer score 2

Hit id144192

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 1
  • Formulasearchengine score: 33673
  • Reference to collection: _PREFIX_/38/f014989.xhtml#id144192
found all required tokens in TeX $Z=\left[\prod _{{N_{m}=1}}^{\infty}{\frac{1+w^{{N_{m}}}}{1-w^{{N_{m}}}}}\right]^{{4N_{1}N_{5}}}\equiv\sum\Omega(N_{m})w^{{N_{m}}}\,,$ at pos:1420460(73%) Scoringfunction: ' + TeX_HIT_SCORE + 1.5 * WORD_SCORE[diverges] + 1.5 * TOKEN_SCORE[+] + 1.9921875 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.9375 * TOKEN_SCORE[1] + 1.998046875 * TOKEN_SCORE[\] + 1.99609375 * TOKEN_SCORE[_] + 1.96875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+1.5*137.070458528965+1.5*0.0160883895861106+1.9921875*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.9375*0.0102451205633244+1.998046875*5.92879328325965E-4+1.99609375*0.00257082788077282+1.96875*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = 33673.197194851746' final score ~ 33673 reviewer: xxx gave 2
Rendered MathML:
Z=Nm=11+wNm1-wNm4N1N5ΩNmwNm,ZsuperscriptsuperscriptsubscriptsubscriptNm11superscriptwsubscriptNm1superscriptwsubscriptNm4subscriptN1subscriptN5ΩsubscriptNmsuperscriptwsubscriptNmZ=\left[\prod _{{N_{m}=1}}^{\infty}{\frac{1+w^{{N_{m}}}}{1-w^{{N_{m}}}}}\right]^{{4N_{1}N_{5}}}\equiv\sum\Omega(N_{m})w^{{N_{m}}}\,,
End of MathML
.

Hit id120502

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 2
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/155/f061772.xhtml#id120502
no match at pos:1016175(000091%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
NNT1/N=pPT1+1/p+1/p2+<.subscriptNsubscriptNT1NsubscriptpsubscriptPT11p1superscriptp2
End of MathML
.

Hit id137326

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 3
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/216/f086170.xhtml#id137326
no match at pos:1250766(000093%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Ω=1ZN=ZNNΩsuperscriptsubscript1subscriptZNsuperscriptsubscriptZNN
End of MathML
.

Hit id140942

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 4
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/157/f062788.xhtml#id140942
no match at pos:1340963(000083%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ZϵZ0=r=11+LrZϵsubscriptZ0superscriptsubscriptr11subscriptLr
End of MathML
.

Hit id144989

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 5
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/157/f062788.xhtml#id144989
no match at pos:1408827(000088%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Z(J=1)Z0=r=11+CrZ(J=1)subscriptZ0superscriptsubscriptr11subscriptCr
End of MathML
.

Hit id55976

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 6
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/106/f042392.xhtml#id55976
no match at pos:41659(000029%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Z=x0,1Nexpi=1Nμ+βνixii,jC1-xixj,Zsubscriptxsuperscript01Nsuperscriptsubscripti1NμβsubscriptνisubscriptxisubscriptijC1subscriptxisubscriptxj
End of MathML
.

Hit id57270

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 7
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/134/f053575.xhtml#id57270
no match at pos:59473(000032%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
q1q5n=11+wn/q1,q5LCM1-wn/q1,q5LCM4Nq11Nq55.subscriptsubscriptq1subscriptsubscriptq5superscriptsubscriptn1superscript1superscriptwnsubscriptsubscriptq1subscriptq5LCM1superscriptwnsubscriptsubscriptq1subscriptq5LCM4superscriptsubscriptNsubscriptq11superscriptsubscriptNsubscriptq55
End of MathML
.

Hit id59779

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 8
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/216/f086035.xhtml#id59779
no match at pos:90655(000015%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
i=1πNZ/2Zsuperscriptsubscripti1πNZ2Z
End of MathML
.

Hit id60579

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 9
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/104/f041448.xhtml#id60579
no match at pos:113094(000012%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Zov=Z01+CrovC,rovC=iCμiβCμβiαC1-miα2,subscriptZovsubscriptZ01subscriptCsubscriptrovCsubscriptrovCsubscriptiCsubscriptμisubscriptβCsubscriptμβsubscriptiαC1superscriptsubscriptmiα2
End of MathML
.

Hit id60771

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 10
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id60771
no match at pos:106265(000041%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
δLN=qLL+/NqM-LLN-C-1n1ZqnC-1n-ej=1N-1mj+njnj,superscriptsubscriptδLNsuperscriptqLLNsubscriptqMLsubscriptLNsubscriptsuperscriptC1n1ZsuperscriptqnsuperscriptC1nsubscriptesuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id61181

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 11
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/24/f009515.xhtml#id61181
no match at pos:120909(000005%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
IS3/Zkp,q=N=0pNINq=N,J=0DS3/ZkN,JpNqJ=IN=4p,qk=1n=01-pqnksubscriptIsuperscriptS3subscriptZkpqsuperscriptsubscriptN0superscriptpNsubscriptINqsuperscriptsubscriptNJ0subscriptDsuperscriptS3subscriptZkNJsuperscriptpNsuperscriptqJsuperscriptsubscriptIN4pqk1subscriptsuperscriptn0superscript1psuperscriptqnk
End of MathML
.

Hit id61792

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 12
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id61792
no match at pos:121426(000047%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
γLN=qLL+/NqM-Lq+1M+LLN-C-1η1ZqηC-1η-ej=1N-1μj+ηjηj,superscriptsubscriptγLNsuperscriptqLLNsubscriptqMLsubscriptsuperscriptq1MLsubscriptLNsubscriptsuperscriptC1η1ZsuperscriptqηsuperscriptC1ηsubscriptesuperscriptsubscriptj1N1subscriptμjsubscriptηjsubscriptηj
End of MathML
.

Hit id63837

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 13
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id63837
no match at pos:153647(000014%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ΔL,k=aL/NqL2/N-kLqM-LnZN-1σqnC-1n-eλj=1N-1mj+njnj.subscriptΔLksuperscriptaLNsuperscriptqsuperscriptL2NkLsubscriptqMLsuperscriptsubscriptnsuperscriptZN1σsuperscriptqnsuperscriptC1nsubscripteλsuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id63933

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 14
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id63933
no match at pos:153202(000059%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
L=0qLL+/NβLLN-C-1n1ZqnC-1n-ej=1N-1mj+njnj,superscriptsubscriptL0superscriptqLLNsubscriptβLsubscriptLNsubscriptsuperscriptC1n1ZsuperscriptqnsuperscriptC1nsubscriptesuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id64671

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 15
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/210/f083781.xhtml#id64671
no match at pos:172628(000041%) VariableMap:[n x 3, sum, N x 5, ( x 3, Omega, m x 2, ) x 3, infty, / x 2, , x 2, -, frac, 2 x 4, 1 x 3, 0, ~, \ x 5, _ x 3, ^ x 8, = x 4, prod, Z, x x 5] Expects 1 occurences for '+' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ZNx=xN2/2m=1N11-xm=xN2/2n=0ΩN,nxn,subscriptZNxsuperscriptxsuperscriptN22superscriptsubscriptm1N11superscriptxmsuperscriptxsuperscriptN22superscriptsubscriptn0ΩNnsuperscriptxnZ_{N}(x)=x^{{N^{2}/2}}\prod _{{m=1}}^{{N}}\frac{1}{(1-x^{m})}=x^{{N^{2}/2}}\sum _{{n=0}}^{{\infty}}\Omega(N,n)x^{n}~,
End of MathML
.

Hit id65913

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 16
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id65913
no match at pos:183249(000071%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
=r1rk0qr12/N+r22++rk2qr1-r2qrk-1-rkqrkr1N-C-1n1ZqnC-1nj=1N-1mj+njnj,subscriptsubscriptr1subscriptrk0superscriptqsuperscriptsubscriptr12Nsuperscriptsubscriptr22superscriptsubscriptrk2subscriptqsubscriptr1subscriptr2subscriptqsubscriptrk1subscriptrksubscriptqsubscriptrksubscriptsubscriptr1NsubscriptsuperscriptC1n1ZsuperscriptqnsuperscriptC1nsuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id66143

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 17
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/123/f048825.xhtml#id66143
no match at pos:173900(000062%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ZωlimNi=1,3j=1,Nπ2aijϵN/2,superscriptsubscriptZωsubscriptNsubscripti13subscriptj1Nsuperscriptπ2subscriptaijϵN2
End of MathML
.

Hit id67293

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 18
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id67293
no match at pos:205914(000019%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
γL=aL/NqL2/NqM-LaqM+LηZN-1σqηC-1η-eλj=1N-1μj+ηjηjsubscriptγLsuperscriptaLNsuperscriptqsuperscriptL2NsubscriptqMLsubscriptaqMLsuperscriptsubscriptηsuperscriptZN1σsuperscriptqηsuperscriptC1ηsubscripteλsuperscriptsubscriptj1N1subscriptμjsubscriptηjsubscriptηj
End of MathML
.

Hit id67313

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 19
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/11/f004382.xhtml#id67313
no match at pos:205274(000020%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Homi=1Z,Zi=1ZHomsuperscriptsubscripti1ZZsuperscriptsubscripti1Z
End of MathML
.

Hit id67812

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 20
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id67812
no match at pos:213766(000020%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
δL=aL/NqL2/NqM-LnZN-1σqnC-1n-eλj=1N-1mj+njnj.subscriptδLsuperscriptaLNsuperscriptqsuperscriptL2NsubscriptqMLsuperscriptsubscriptnsuperscriptZN1σsuperscriptqnsuperscriptC1nsubscripteλsuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id72049

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 21
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id72049
no match at pos:277765(000026%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
η,iZN-1σ,Lq-iC-1i+2L+e1ki1/qqηC-1η-eλj=1N-1ηj+μjηjsuperscriptsubscriptηisuperscriptZN1σLsuperscriptqisuperscriptC1i2Lsubscripte1subscriptki1qsuperscriptqηsuperscriptC1ηsubscripteλsuperscriptsubscriptj1N1superscriptsubscriptηjsubscriptμjsubscriptηj
End of MathML
.

Hit id73235

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 22
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/135/f053793.xhtml#id73235
no match at pos:302607(000084%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
pk=1Znk+1=1nN=nN-1xnk+1+nk+2++nN=xN-ki=0k-11-xN-i.subscriptpk1Zsuperscriptsubscriptsubscriptnk11superscriptsubscriptsubscriptnNsubscriptnN1superscriptxsubscriptnk1subscriptnk2subscriptnNsuperscriptxNksuperscriptsubscripti0k11superscriptxNi
End of MathML
.

Hit id76993

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 23
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/233/f092933.xhtml#id76993
no match at pos:351894(000045%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
GNCQ2YY=e2MZ2Q2+MW2Q2MW2Q2+MZ2w=1NQ2+mWw2mWw2z=1NmZz2Q2+mZz2.subscriptsubscriptGNCsuperscriptQ2YYsuperscripte2subscriptsuperscriptM2ZsuperscriptQ2subscriptsuperscriptM2WsuperscriptQ2subscriptsuperscriptM2WsuperscriptQ2subscriptsuperscriptM2Zsuperscriptsubscriptw1NsuperscriptQ2subscriptsuperscriptm2Wwsubscriptsuperscriptm2Wwsuperscriptsubscriptz1Nsubscriptsuperscriptm2ZzsuperscriptQ2subscriptsuperscriptm2Zz
End of MathML
.

Hit id78502

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 24
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id78502
no match at pos:374701(000035%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
=qM+L+M-L-NM-L/NnZN-1σ,MqnC-1n-eλj=1N-1mj+njnjsuperscriptqMLMLNMLNsuperscriptsubscriptnsuperscriptZN1σMsuperscriptqnsuperscriptC1nsubscripteλsuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit id79632

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 25
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/57/f022620.xhtml#id79632
no match at pos:387994(000058%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Ni=1R--1i+1qNN-1-N-i+1N-iZ,whereZ=±q-N-12/2.subscriptsuperscriptNi1Rsuperscript1i1superscriptqNN1Ni1NiZwhereZ±superscriptqsuperscriptN122
End of MathML
.

Hit id82887

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 26
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/135/f053801.xhtml#id82887
no match at pos:444759(000078%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Z=z124mZ2z2m+ix+Ny2n=11-zn-1.Zsuperscriptz124superscriptsubscriptmZ2superscriptz2superscriptmixNy2superscriptsubscriptn1superscript1superscriptzn1
End of MathML
.

Hit id91421

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 27
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id91421
no match at pos:569144(000053%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
L=0aL/NqL2/NβLnZN-1σ,LqnC-1n-eλj=1N-1mj+njnj,superscriptsubscriptL0superscriptaLNsuperscriptqsuperscriptL2NsubscriptβLsuperscriptsubscriptnsuperscriptZN1σLsuperscriptqnsuperscriptC1nsubscripteλsuperscriptsubscriptj1N1subscriptmjsubscriptnjsubscriptnj
End of MathML
.

Hit idp21725184

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 28
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/15/f005739.xhtml#idp21725184
no match at pos:272901(000019%) VariableMap:[! x 2, n x 2, ( x 2, N x 5, ) x 2, /, h, , x 2, frac, 2 x 2, 1 x 2, 0, t, P, p, \ x 4, _ x 4, ^ x 3, pi, = x 3, prod x 2, Z] Expects 1 occurences for '+' but has only 0 Expects 1 occurences for 'infty' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Z(t,N)=N!(2π)N/2p=1NP!n=0N1hn,ZtNNsuperscript2πN2superscriptsubscriptproductp1NPsuperscriptsubscriptproductn0subscriptN1subscripthnZ(t,N)=\frac{N!}{(2\pi)^{{N/2}}\prod _{{p=1}}^{N}P!}\prod _{{n=0}}^{{N_{1}}}h_{n},
End of MathML
.

Hit id55977

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 78
  • Formulasearchengine score: -9986151
  • Reference to collection: _PREFIX_/36/f014207.xhtml#id55977
found all required tokens in TeX $Z^{{(\beta)}}_{\nu}=\prod _{{i=1}}^{{N_{f}}}m_{i}^{\nu}\int _{0}^{\infty}\prod _{{i=1}}^{N}\Bigl(dx_{i}\, x_{i}^{{\beta(\nu+1)/2-1}}e^{{-\beta x_{i}}}\prod _{{j=1}}^{{N_{f}}}(x_{i}+m_{j}^{2})\Bigr)\prod _{{i>j}}^{N}|x_{i}-x_{j}|^{\beta}~,$ at pos:36927(16%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.9375 * TOKEN_SCORE[N] + 1.9375 * TOKEN_SCORE[(] + 1.9375 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.96875 * TOKEN_SCORE[1] + 1.9999847412109375 * TOKEN_SCORE[\] + 1.9999847412109375 * TOKEN_SCORE[_] + 1.99951171875 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[=] + 1.9375 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.9375*0.367378648065486+1.9375*0.00418257496311516+1.9375*0.00417601612706465+1.5*0.184871254938806+1.5*0.382802832581921+1.96875*0.0102451205633244+1.9999847412109375*5.92879328325965E-4+1.9999847412109375*0.00257082788077282+1.99951171875*0.00338742677192689+1.9375*2.678806489+1.9375*15.4961284798907+1.5*1.08914121500786 = -9986151.142431458' final score ~ -9986151 reviewer: xxx gave 2
Rendered MathML:
Zνβ=i=1Nfmiν0i=1Ndxixiβν+1/2-1e-βxij=1Nfxi+mj2i>jNxi-xjβ,subscriptsuperscriptZβνsuperscriptsubscripti1subscriptNfsuperscriptsubscriptmiνsuperscriptsubscript0superscriptsubscripti1Ndsubscriptxisuperscriptsubscriptxiβν121superscripteβsubscriptxisuperscriptsubscriptj1subscriptNfsubscriptxisuperscriptsubscriptmj2superscriptsubscriptijNsuperscriptsubscriptxisubscriptxjβZ^{{(\beta)}}_{\nu}=\prod _{{i=1}}^{{N_{f}}}m_{i}^{\nu}\int _{0}^{\infty}\prod _{{i=1}}^{N}\Bigl(dx_{i}\, x_{i}^{{\beta(\nu+1)/2-1}}e^{{-\beta x_{i}}}\prod _{{j=1}}^{{N_{f}}}(x_{i}+m_{j}^{2})\Bigr)\prod _{{i>j}}^{N}|x_{i}-x_{j}|^{\beta}~,
End of MathML
.

Hit idp4604736

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 79
  • Formulasearchengine score: -9986286
  • Reference to collection: _PREFIX_/132/f052670.xhtml#idp4604736
found all required tokens in TeX $Z_{{\rm BPS}}^{{\rm closed}}:=\prod _{{\beta>0}}\prod _{{j_{L},j_{R}\in{\mathbb{Z}}/2}}\prod _{{n_{1},n_{2}=0}}^{\infty}\left(1-q_{1}^{{j_{L}+j_{R}+n_{1}+\frac{1}{2}}}q_{2}^{{j_{L}-j_{R}+n_{2}+\frac{1}{2}}}Q^{\beta}\right)^{{(-1)^{{2j_{L}+2j_{R}}}N^{{j_{L},j_{R}}}_{{\beta}}}}\,$ at pos:600266(29%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.984375 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.9921875 * TOKEN_SCORE[1] + 1.9999847412109375 * TOKEN_SCORE[\] + 1.9999995231628418 * TOKEN_SCORE[_] + 1.99609375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.875 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.984375*0.0160883895861106+1.5*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.5*0.184871254938806+1.5*0.382802832581921+1.9921875*0.0102451205633244+1.9999847412109375*5.92879328325965E-4+1.9999995231628418*0.00257082788077282+1.99609375*0.00338742677192689+1.75*2.678806489+1.875*15.4961284798907+1.75*1.08914121500786 = -9986286.821935566' final score ~ -9986286 reviewer: xxx gave 2
Rendered MathML:
ZBPSclosed:=β>0jL,jR/2n1,n2=0(1-q1jL+jR+n1+12q2jL-jR+n2+12Qβ)(-1)2jL+2jRNβjL,jRassignsuperscriptsubscriptZBPSclosedsubscriptproductβ0subscriptproductsubscriptjLsubscriptjRZ2superscriptsubscriptproductsubscriptn1subscriptn20superscript1superscriptsubscriptq1subscriptjLsubscriptjRsubscriptn112superscriptsubscriptq2subscriptjLsubscriptjRsubscriptn212superscriptQβsuperscript12subscriptjL2subscriptjRsubscriptsuperscriptNsubscriptjLsubscriptjRβZ_{{\rm BPS}}^{{\rm closed}}:=\prod _{{\beta>0}}\prod _{{j_{L},j_{R}\in{\mathbb{Z}}/2}}\prod _{{n_{1},n_{2}=0}}^{\infty}\left(1-q_{1}^{{j_{L}+j_{R}+n_{1}+\frac{1}{2}}}q_{2}^{{j_{L}-j_{R}+n_{2}+\frac{1}{2}}}Q^{\beta}\right)^{{(-1)^{{2j_{L}+2j_{R}}}N^{{j_{L},j_{R}}}_{{\beta}}}}\,
End of MathML
.

Hit idp4909712

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 80
  • Formulasearchengine score: -9986287
  • Reference to collection: _PREFIX_/132/f052670.xhtml#idp4909712
found all required tokens in TeX $Z^{{\rm open}}_{{\rm BPS}}=\prod _{{\mu>0}}\prod _{{s,r\in\mathbb{Z}/2}}\prod _{{n=0}}^{\infty}\left(1-q_{1}^{{s+n+\frac{1}{2}}}q_{2}^{{r+\frac{1}{2}}}z^{\mu}\right)^{{-(-1)^{{2s}}N_{{\mu}}^{{s,r}}}}\,.$ at pos:640275(30%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.875 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.96875 * TOKEN_SCORE[1] + 1.9999847412109375 * TOKEN_SCORE[\] + 1.9921875 * TOKEN_SCORE[_] + 1.99609375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.875 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.875*0.0160883895861106+1.5*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.5*0.184871254938806+1.5*0.382802832581921+1.96875*0.0102451205633244+1.9999847412109375*5.92879328325965E-4+1.9921875*0.00257082788077282+1.99609375*0.00338742677192689+1.75*2.678806489+1.875*15.4961284798907+1.75*1.08914121500786 = -9986287.023922663' final score ~ -9986287 reviewer: xxx gave 2
Rendered MathML:
ZBPSopen=μ>0s,r/2n=0(1-q1s+n+12q2r+12zμ)-(-1)2sNμs,r.subscriptsuperscriptZopenBPSsubscriptproductμ0subscriptproductsrZ2superscriptsubscriptproductn0superscript1superscriptsubscriptq1sn12superscriptsubscriptq2r12superscriptzμsuperscript12ssuperscriptsubscriptNμsrZ^{{\rm open}}_{{\rm BPS}}=\prod _{{\mu>0}}\prod _{{s,r\in\mathbb{Z}/2}}\prod _{{n=0}}^{\infty}\left(1-q_{1}^{{s+n+\frac{1}{2}}}q_{2}^{{r+\frac{1}{2}}}z^{\mu}\right)^{{-(-1)^{{2s}}N_{{\mu}}^{{s,r}}}}\,.
End of MathML
.

Hit id86637

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 81
  • Formulasearchengine score: -9986481
  • Reference to collection: _PREFIX_/140/f055940.xhtml#id86637
found all required tokens in TeX $\sum\limits _{{k\in\mathbb{Z}^{\infty}}}\varphi(k)=\ \ \prod\limits _{{i\in\mathbb{N}}}\sum\limits _{{j\in\mathbb{Z}}}\mu _{i}^{{|j|}}=\ \ \prod\limits _{{i\in\mathbb{N}}}\frac{1+\mu _{i}}{1-\mu _{i}}\ .$ at pos:502778(62%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.75 * TOKEN_SCORE[1] + 1.9999999925494194 * TOKEN_SCORE[\] + 1.9921875 * TOKEN_SCORE[_] + 1.75 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.75 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.75*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.75*0.0102451205633244+1.9999999925494194*5.92879328325965E-4+1.9921875*0.00257082788077282+1.75*0.00338742677192689+1.75*2.678806489+1.75*15.4961284798907+1.75*1.08914121500786 = -9986481.904378157' final score ~ -9986481 reviewer: xxx gave 2
Rendered MathML:
kZφk=iNjZμij=iN1+μi1-μi.subscriptksuperscriptZφksubscriptiNsubscriptjZsuperscriptsubscriptμijsubscriptiN1subscriptμi1subscriptμi\sum\limits _{{k\in\mathbb{Z}^{\infty}}}\varphi(k)=\ \ \prod\limits _{{i\in\mathbb{N}}}\sum\limits _{{j\in\mathbb{Z}}}\mu _{i}^{{|j|}}=\ \ \prod\limits _{{i\in\mathbb{N}}}\frac{1+\mu _{i}}{1-\mu _{i}}\ .
End of MathML
.

Hit idp4966880

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 83
  • Formulasearchengine score: -9986841
  • Reference to collection: _PREFIX_/19/f007244.xhtml#idp4966880
found all required tokens in TeX $\displaystyle I^{{(n)}}={n}\int^{\infty}_{{-\infty}}\frac{d\lambda}{2\pi}\int^{{-\Delta+(n-1/2)eV}}_{{\Delta-eV/2}}\frac{dE}{eR}\,\frac{N_{{1/2}}N_{{1/2-n}}}{|Z_{K}|}\prod _{{\alpha=1}}^{{n-1}}\frac{a_{{1/2-\alpha}}}{|Z_{{-\alpha}}|},$ at pos:637944(87%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.96875 * TOKEN_SCORE[/] + 1.75 * TOKEN_SCORE[infty] + 1.984375 * TOKEN_SCORE[1] + 1.9999961853027344 * TOKEN_SCORE[\] + 1.99609375 * TOKEN_SCORE[_] + 1.9375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.75*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.96875*0.184871254938806+1.75*0.382802832581921+1.984375*0.0102451205633244+1.9999961853027344*5.92879328325965E-4+1.99609375*0.00257082788077282+1.9375*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.75*1.08914121500786 = -9986841.314513473' final score ~ -9986841 reviewer: xxx gave 2
Rendered MathML:
I(n)=n-dλ2πΔ-eV/2-Δ+(n-1/2)eVdEeRN1/2N1/2-n|ZK|α=1n-1a1/2-α|Z-α|,superscriptInnsubscriptsuperscriptdλ2πsubscriptsuperscriptΔn12eVΔeV2dEeRsubscriptN12subscriptN12nsubscriptZKsuperscriptsubscriptproductα1n1subscripta12αsubscriptZα\displaystyle I^{{(n)}}={n}\int^{\infty}_{{-\infty}}\frac{d\lambda}{2\pi}\int^{{-\Delta+(n-1/2)eV}}_{{\Delta-eV/2}}\frac{dE}{eR}\,\frac{N_{{1/2}}N_{{1/2-n}}}{|Z_{K}|}\prod _{{\alpha=1}}^{{n-1}}\frac{a_{{1/2-\alpha}}}{|Z_{{-\alpha}}|},
End of MathML
.

Hit id70616

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 84
  • Formulasearchengine score: -9986843
  • Reference to collection: _PREFIX_/168/f066981.xhtml#id70616
found all required tokens in TeX $\sum _{{N_{c}=1}}^{\infty}P(N_{c})=\frac{1}{2\sqrt{3}}\prod _{{n=1}}^{\infty}(1-{\tilde{q}}^{{2n}})^{{-1}}\sum _{{p\in{\bf Z}}}\left(\cos\textstyle{\pi p\over 6}\displaystyle+\cos\textstyle{5\pi p\over 6}\displaystyle-2\cos\textstyle{\pi p\over 2}\displaystyle\right)\,{\tilde{q}}^{{(p^{2}-1)/12}}$ at pos:264529(73%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.9375 * TOKEN_SCORE[(] + 1.9375 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.75 * TOKEN_SCORE[infty] + 1.9921875 * TOKEN_SCORE[1] + 1.9999999981373549 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[_] + 1.984375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.75*0.367378648065486+1.9375*0.00418257496311516+1.9375*0.00417601612706465+1.5*0.184871254938806+1.75*0.382802832581921+1.9921875*0.0102451205633244+1.9999999981373549*5.92879328325965E-4+1.96875*0.00257082788077282+1.984375*0.00338742677192689+1.875*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986843.550226048' final score ~ -9986843 reviewer: xxx gave 2
Rendered MathML:
Nc=1PNc=123n=11-q~2n-1pZcosπp6+cos5πp6-2cosπp2q~p2-1/12superscriptsubscriptsubscriptNc1PsubscriptNc123superscriptsubscriptn1superscript1superscript~q2n1subscriptpZπp65πp62πp2superscript~qsuperscriptp2112\sum _{{N_{c}=1}}^{\infty}P(N_{c})=\frac{1}{2\sqrt{3}}\prod _{{n=1}}^{\infty}(1-{\tilde{q}}^{{2n}})^{{-1}}\sum _{{p\in{\bf Z}}}\left(\cos\textstyle{\pi p\over 6}\displaystyle+\cos\textstyle{5\pi p\over 6}\displaystyle-2\cos\textstyle{\pi p\over 2}\displaystyle\right)\,{\tilde{q}}^{{(p^{2}-1)/12}}
End of MathML
.

Hit idp20672624

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 88
  • Formulasearchengine score: -9986868
  • Reference to collection: _PREFIX_/115/f045952.xhtml#idp20672624
found all required tokens in TeX $\displaystyle{\cal Z}_{{CS}}^{{m=n=0}}=\frac{1}{(k+N)^{{N/2}}}\prod _{{\alpha>0}}2\sinh\left(\frac{2\pi i}{k+N}\frac{\alpha\cdot\rho}{2}\right),$ at pos:127108(8%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.875 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.5 * TOKEN_SCORE[1] + 1.99993896484375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[_] + 1.75 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.875*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.5*0.184871254938806+1.0*0.382802832581921+1.5*0.0102451205633244+1.99993896484375*5.92879328325965E-4+1.75*0.00257082788077282+1.75*0.00338742677192689+1.875*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986868.062604554' final score ~ -9986868 reviewer: xxx gave 2
Rendered MathML:
ZCSm=n=0=1(k+N)N/2α>02sinh(2πik+Nαρ2),superscriptsubscriptZCSmn01superscriptkNN2subscriptproductα022πikNαρ2\displaystyle{\cal Z}_{{CS}}^{{m=n=0}}=\frac{1}{(k+N)^{{N/2}}}\prod _{{\alpha>0}}2\sinh\left(\frac{2\pi i}{k+N}\frac{\alpha\cdot\rho}{2}\right),
End of MathML
.

Hit id71446

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 91
  • Formulasearchengine score: -9986894
  • Reference to collection: _PREFIX_/36/f014160.xhtml#id71446
found all required tokens in TeX $Z_{N}=x^{{gN(N-1)/2+N/2}}\prod _{{j=1}}^{N}\frac{1}{(1-x^{j})},$ at pos:277402(69%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.9375 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.75 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.9375 * TOKEN_SCORE[1] + 1.75 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[_] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.9375*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.75*0.184871254938806+1.0*0.382802832581921+1.9375*0.0102451205633244+1.75*5.92879328325965E-4+1.75*0.00257082788077282+1.875*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986894.556248987' final score ~ -9986894 reviewer: xxx gave 2
Rendered MathML:
ZN=xgNN-1/2+N/2j=1N11-xj,subscriptZNsuperscriptxgNN12N2superscriptsubscriptj1N11superscriptxjZ_{N}=x^{{gN(N-1)/2+N/2}}\prod _{{j=1}}^{N}\frac{1}{(1-x^{j})},
End of MathML
.

Hit idp25519280

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 92
  • Formulasearchengine score: -9986906
  • Reference to collection: _PREFIX_/11/f004111.xhtml#idp25519280
found all required tokens in TeX $\prod _{{n=1}}^{\infty}(1-q^{n})(1+q^{{n-1/2}}t)(1+q^{{n-1/2}}t^{{-1}})=\sum _{{n\in{\bf Z}}}q^{{n^{2}/2}}t^{n}$ at pos:787293(45%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.0 * TOKEN_SCORE[N] + 1.875 * TOKEN_SCORE[(] + 1.875 * TOKEN_SCORE[)] + 1.875 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.9921875 * TOKEN_SCORE[1] + 1.96875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[_] + 1.99609375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.0*0.367378648065486+1.875*0.00418257496311516+1.875*0.00417601612706465+1.875*0.184871254938806+1.5*0.382802832581921+1.9921875*0.0102451205633244+1.96875*5.92879328325965E-4+1.75*0.00257082788077282+1.99609375*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986906.93025594' final score ~ -9986906 reviewer: xxx gave 2
Rendered MathML:
n=11-qn1+qn-1/2t1+qn-1/2t-1=nZqn2/2tnsuperscriptsubscriptproductn11superscriptqn1superscriptqn12t1superscriptqn12superscriptt1subscriptnZsuperscriptqsuperscriptn22superscripttn\prod _{{n=1}}^{\infty}(1-q^{n})(1+q^{{n-1/2}}t)(1+q^{{n-1/2}}t^{{-1}})=\sum _{{n\in{\bf Z}}}q^{{n^{2}/2}}t^{n}
End of MathML
.

Hit id109349

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 94
  • Formulasearchengine score: -9986910
  • Reference to collection: _PREFIX_/26/f010285.xhtml#id109349
found all required tokens in TeX $I(f)\big|_{{{\mathbb{L}}=1}}=\sum _{{I\subset{\rm irr}(D)}}\rho[\tilde{E}_{I}^{\circ}/X;{\bf\mu}_{{N(I)}}]\prod _{{i\in I}}\frac{1}{\nu _{i}+sN_{i}}\in M_{X}({\hat{\bf\mu}})/({\mathbb{L}}-1)\otimes _{{\mathbb{Z}}}{\mathbb{Q}}(s).$ at pos:885714(50%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[N] + 1.984375 * TOKEN_SCORE[(] + 1.984375 * TOKEN_SCORE[)] + 1.75 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.875 * TOKEN_SCORE[1] + 1.999999761581421 * TOKEN_SCORE[\] + 1.998046875 * TOKEN_SCORE[_] + 1.5 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.5*0.367378648065486+1.984375*0.00418257496311516+1.984375*0.00417601612706465+1.75*0.184871254938806+1.0*0.382802832581921+1.875*0.0102451205633244+1.999999761581421*5.92879328325965E-4+1.998046875*0.00257082788077282+1.5*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986910.545630315' final score ~ -9986910 reviewer: xxx gave 2
Rendered MathML:
IfL=1=IirrDρE~I/X;μNIiI1νi+sNiMXμ/L-1ZQs.IfL1subscriptIirrDρsuperscriptsubscript~EIXsubscriptμNIsubscriptiI1subscriptνissubscriptNisubscriptZsubscriptMXμL1QsI(f)\big|_{{{\mathbb{L}}=1}}=\sum _{{I\subset{\rm irr}(D)}}\rho[\tilde{E}_{I}^{\circ}/X;{\bf\mu}_{{N(I)}}]\prod _{{i\in I}}\frac{1}{\nu _{i}+sN_{i}}\in M_{X}({\hat{\bf\mu}})/({\mathbb{L}}-1)\otimes _{{\mathbb{Z}}}{\mathbb{Q}}(s).
End of MathML
.

Hit id186007

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 96
  • Formulasearchengine score: -9986923
  • Reference to collection: _PREFIX_/208/f083176.xhtml#id186007
found all required tokens in TeX $(\prod _{{n=1}}^{{\infty}}(1-x^{n}))^{{dim\, K}}=\sum _{{k\in\mathbb{Z}_{+}}}b_{k}\, x^{{k}}$ at pos:1935316(86%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.0 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.75 * TOKEN_SCORE[1] + 1.9921875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[_] + 1.9375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.0*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.75*0.0102451205633244+1.9921875*5.92879328325965E-4+1.9375*0.00257082788077282+1.9375*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986923.831562508' final score ~ -9986923 reviewer: xxx gave 2
Rendered MathML:
n=11-xndimK=kZ+bkxksuperscriptsuperscriptsubscriptn11superscriptxndimKsubscriptksubscriptZsubscriptbksuperscriptxk(\prod _{{n=1}}^{{\infty}}(1-x^{n}))^{{dim\, K}}=\sum _{{k\in\mathbb{Z}_{+}}}b_{k}\, x^{{k}}
End of MathML
.

Hit id67090

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 97
  • Formulasearchengine score: -9986976
  • Reference to collection: _PREFIX_/168/f066981.xhtml#id67090
found all required tokens in TeX $\displaystyle C_{5}\, q^{{-\frac{1}{24}}}\prod _{{n=1}}^{\infty}(1-q^{n})^{{-1}}\sum _{{r\in{\bf Z}}}e^{{-((3\chi^{{\prime}}+2\pi r)^{2})/\pi g)(\ell/L)}}$ at pos:210048(58%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.0 * TOKEN_SCORE[N] + 1.9375 * TOKEN_SCORE[(] + 1.96875 * TOKEN_SCORE[)] + 1.75 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.9375 * TOKEN_SCORE[1] + 1.9998779296875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[_] + 1.9921875 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.0*0.367378648065486+1.9375*0.00418257496311516+1.96875*0.00417601612706465+1.75*0.184871254938806+1.5*0.382802832581921+1.9375*0.0102451205633244+1.9998779296875*5.92879328325965E-4+1.875*0.00257082788077282+1.9921875*0.00338742677192689+1.5*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986976.571597701' final score ~ -9986976 reviewer: xxx gave 2
Rendered MathML:
C5q-124n=11-qn-1rZe-((3χ+2πr)2)/πg)(/L)subscriptC5superscriptq124superscriptsubscriptn1superscript1superscriptqn1subscriptrZsuperscripte-((3χ′+2πr)2)/πg)(ℓ/L)\displaystyle C_{5}\, q^{{-\frac{1}{24}}}\prod _{{n=1}}^{\infty}(1-q^{n})^{{-1}}\sum _{{r\in{\bf Z}}}e^{{-((3\chi^{{\prime}}+2\pi r)^{2})/\pi g)(\ell/L)}}
End of MathML
.

Detailed results for reviewer score 0

Hit id104602

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 29
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id104602
no match at pos:770968(000072%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1qj=--1jq2k+δ-2+2/Nj+2k-2i+δj/2ηZN-1σ,jqηC-1η-eλqη1qηN-11subscriptqsuperscriptsubscriptjsuperscript1jsuperscriptq2kδ22Nj2k2iδj2superscriptsubscriptηsuperscriptZN1σjsuperscriptqηsuperscriptC1ηsubscripteλsubscriptqsubscriptη1subscriptqsubscriptηN1
End of MathML
.

Hit id108891

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 30
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/214/f085431.xhtml#id108891
no match at pos:859635(000061%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
LN=1+oP1t1xZexp-ANt,x-BNt,x-CNt,x/2subscriptLN1subscriptoP1subscriptt1subscriptxZsubscriptANtxsubscriptBNtxsubscriptCNtx2
End of MathML
.

Hit id119596

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 31
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/145/f057798.xhtml#id119596
no match at pos:999911(000093%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1aqp-p=0N/2ηZN-12p-λ+σN2N-C-1η1ZqηC-1η-eλqη1qηN-1L=0L+/2±pmodNaL/NqL2/NαL,1subscriptaqsuperscriptsubscriptpsubscriptp0N2subscriptηsuperscriptZN12pλσN2NsubscriptsuperscriptC1η1ZsuperscriptqηsuperscriptC1ηsubscripteλsubscriptqsubscriptη1subscriptqsubscriptηN1superscriptsubscript=L0≡+L/ℓ2±pNmodsuperscriptaLNsuperscriptqsuperscriptL2NsubscriptαL
End of MathML
.

Hit id142636

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 32
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/88/f035117.xhtml#id142636
no match at pos:1378910(000080%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Z~nC1NM=02πVμ2/NA2MM!e=1Mje,aeje,aee=1Mδ3cje+12sje,ae-cje-12sje,aeΔ2sje,ae+sje,aeN,1n+1.superscript~ZnC1NsuperscriptsubscriptM0superscript2πVsuperscriptμ2NsuperscriptA2MMsuperscriptsubscripte1Msubscriptsubscriptjesubscriptaesubscriptsubscriptsuperscriptjesubscriptsuperscriptaesuperscriptsubscriptsuperscriptsubscripte1Msuperscriptδ3subscriptcsubscriptje12subscriptssubscriptjesubscriptaesubscriptcsuperscriptsubscriptje12subscriptssuperscriptsubscriptjesuperscriptsubscriptaesuperscriptΔ2subscriptssubscriptjesubscriptaesubscriptssuperscriptsubscriptjesuperscriptsubscriptaeN1n1
End of MathML
.

Hit id191810

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 33
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/180/f071870.xhtml#id191810
no match at pos:2144184(000092%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
κ1NZ/ZCvκsubscriptκ1NZZCsubscriptvκ
End of MathML
.

Hit id201824

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 34
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/180/f071870.xhtml#id201824
no match at pos:2303902(000099%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
ai1NZ/Ztx+i+c=0asubscripti1NZZtxic0
End of MathML
.

Hit id54662

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 35
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/53/f021034.xhtml#id54662
no match at pos:15151(000019%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
KAK1+cA-1/3+KτN-Z/A2+KCoulZ2A-4/3.subscriptKAsubscriptK1csuperscriptA13subscriptKτsuperscriptNZA2subscriptKCoulsuperscriptZ2superscriptA43
End of MathML
.

Hit id55122

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 36
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/1/f000106.xhtml#id55122
no match at pos:23763(000005%) VariableMap:[Im, mathbb, C, M, mathrm, (, N x 3, ), ., in, , x 5, 1, 0, \ x 13, left x 2, _ x 3, |, ^, dots, right x 2, = x 2, Z x 3] Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 1 Expects 1 occurences for 'prod' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
M=Z1,,ZNCN|ImZN=0MsubscriptZ1subscriptZNsuperscriptCNImsubscriptZN0M=\left\{(Z_{1},\dots,Z_{N})\in\mathbb{C}^{N}\,\left|\,\mathrm{Im}\, Z_{N}=0\right.\right\}
End of MathML
.

Hit id55628

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 37
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/40/f015755.xhtml#id55628
no match at pos:35749(000010%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Zμ=N=1ZNexp-μNZμsuperscriptsubscriptN1subscriptZNμN
End of MathML
.

Hit id57272

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 38
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/22/f008679.xhtml#id57272
no match at pos:59408(000012%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
VnnNnZ+Vn:ιVn=Vn-1,nNsubscriptsubscriptVnnNsubscriptnsubscriptZsubscriptVnιsubscriptVnsubscriptVn1nN
End of MathML
.

Hit id59184

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 39
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033485.xhtml#id59184
no match at pos:86851(000008%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
EN,ZclA=infΨ,HN,ZclAΨ:Ψ1NC0R3C2,Ψ=1,superscriptsubscriptENZclAinfΨsuperscriptsubscriptHNZclAΨΨsuperscriptsubscript1NsuperscriptsubscriptC0superscriptR3superscriptC2Ψ1
End of MathML
.

Hit id60238

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 40
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033485.xhtml#id60238
no match at pos:102782(000009%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
EN,Zqed=infΨ,HN,ZqedΨ:Ψ1NC0R3C2F,Ψ=1.superscriptsubscriptENZqedinfΨsuperscriptsubscriptHNZqedΨΨsuperscriptsubscript1NsuperscriptsubscriptC0superscriptR3superscriptC2FΨ1
End of MathML
.

Hit id60376

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 41
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/34/f013566.xhtml#id60376
no match at pos:106632(000061%) VariableMap:[to, f, ln, 1, lim, \ x 4, ( x 2, N x 3, _ x 2, ) x 2, /, infty, =, Z] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for '1' but has only 1 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for 'prod' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
f=limN1/NlnZNfsubscriptN1NsubscriptZNf=\lim _{{N\to\infty}}(1/N)\ln(Z_{N})
End of MathML
.

Hit id60591

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 42
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/214/f085506.xhtml#id60591
no match at pos:107843(000014%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Z0=limNWP1PNPsgnPn=12NSPn,nsubscriptZ0subscriptNWsubscriptP1subscriptPNsubscriptPsgnPsuperscriptsubscriptn12NsubscriptSPnn
End of MathML
.

Hit id60735

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 43
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/82/f032605.xhtml#id60735
no match at pos:108763(000011%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1-PN*Z1subscriptPNZ
End of MathML
.

Hit id61182

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 44
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f071075.xhtml#id61182
no match at pos:118333(000044%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
vt=logZN+1t/ZNtvtsubscriptZN1tsubscriptZNt
End of MathML
.

Hit id62678

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 45
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/182/f072602.xhtml#id62678
no match at pos:144028(000027%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Zb=Z0N=0-b/2NN!i=1Ndxidxidyii=1Nδd-1hxi,yi-hxi,yi0,subscriptZbsubscriptZ0superscriptsubscriptN0superscriptb2NNsuperscriptsubscripti1Ndsubscriptxidsubscriptsuperscriptxidsubscriptyisubscriptsuperscriptsubscripti1Nsuperscriptδd1hsubscriptxisubscriptyihsubscriptsuperscriptxisubscriptyi0
End of MathML
.

Hit id62687

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 46
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f071068.xhtml#id62687
no match at pos:139307(000059%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
expNVeffCEL,σ=12k=12sx,sxZN-xdσxexpγL2x,nsxsx+n+VIMNsuperscriptsubscriptVeffCELσ12superscriptsubscriptk12subscriptsubscriptsxsubscriptsxZNsuperscriptsubscriptsubscriptxdsubscriptσxγsuperscriptL2subscriptxnsubscriptsxsubscriptsxnsubscriptVIM
End of MathML
.

Hit id63367

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 47
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/79/f031523.xhtml#id63367
no match at pos:149717(000006%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
EwiGZg=hGZ/Ni=1raigh-wisubscriptsuperscriptEGZsubscriptwigsubscripthGZNsuperscriptsubscripti1rsubscriptaisuperscriptghsubscriptwi
End of MathML
.

Hit id63388

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 48
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id63388
no match at pos:144977(000056%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1q+1L=0qLL+/NαLLN-C-1η1ZqηC-1η-eqη1qηN-11subscriptsuperscriptq1superscriptsubscriptL0superscriptqLLNsubscriptαLsubscriptLNsubscriptsuperscriptC1η1ZsuperscriptqηsuperscriptC1ηsubscriptesubscriptqsubscriptη1subscriptqsubscriptηN1
End of MathML
.

Hit id63491

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 49
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/248/f099117.xhtml#id63491
no match at pos:151352(000037%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Z=j=1Zj+Zj-,Zsuperscriptsubscriptj1superscriptsubscriptZjsuperscriptsubscriptZj
End of MathML
.

Hit id64607

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 50
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id64607
no match at pos:163194(000063%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1qj=--1jq1+2/Nj+1j/2jN-C-1η1ZqηC-1ηqη1qηN-1=1.1subscriptqsuperscriptsubscriptjsuperscript1jsuperscriptq12Nj1j2subscriptjNsubscriptsuperscriptC1η1ZsuperscriptqηsuperscriptC1ηsubscriptqsubscriptη1subscriptqsubscriptηN11.
End of MathML
.

Hit id65057

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 51
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/249/f099318.xhtml#id65057
no match at pos:174878(000093%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
i=m+1N-1CiN.superscriptsubscriptim1N1subscriptsuperscriptCNi
End of MathML
.

Hit id65400

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 52
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/178/f070808.xhtml#id65400
no match at pos:175316(000067%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1qj=--1jq2k+1+2/Nj+1j/2jN-C-1η1ZqηC-1ηqη1qηN-11subscriptqsuperscriptsubscriptjsuperscript1jsuperscriptq2k12Nj1j2subscriptjNsubscriptsuperscriptC1η1ZsuperscriptqηsuperscriptC1ηsubscriptqsubscriptη1subscriptqsubscriptηN1
End of MathML
.

Hit id66381

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 53
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/52/f020521.xhtml#id66381
no match at pos:194358(000040%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
DηV:=limNi=1Ndviγvi3-ηZηt/2DN.:=subscriptDηVsubscriptNsuperscriptsubscripti1Ndsubscriptviγsuperscriptsubscriptvi3ηsubscriptZηt2DN
End of MathML
.

Hit id67244

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 54
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/217/f086434.xhtml#id67244
no match at pos:206767(000038%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
limN1NalogEZn+1Wa/n+1=Pa.subscriptN1NaEsubscriptZn1superscriptWan1Pa
End of MathML
.

Hit id67479

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 55
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/207/f082789.xhtml#id67479
no match at pos:218435(000018%) VariableMap:[setminus x 2, F x 5, mathbb x 4, C x 2, N x 2, ( x 4, ) x 4, bigcap, in x 2, I, rtimes x 2, 1, textstyle x 2, 0 x 3, mathcal, p x 4, ;, \ x 21, _ x 8, ^ x 2, big x 4, = x 2, prod, Z x 3] Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
I1=C0pFZFZpNF=C0pFZp0NF;subscriptI1subscriptC0subscriptpFsubscriptZFsubscriptZpsuperscriptNFsubscriptC0subscriptpFsubscriptZp0superscriptNFI_{1}=C_{0}\big(\textstyle{\bigcap _{{p\in F}}}({\mathbb{Z}}_{F}\setminus{\mathcal{Z}}_{p})\big)\rtimes{\mathbb{N}}^{F}=C_{0}\big(\textstyle{\prod _{{p\in F}}}({{\mathbb{Z}}_{p}}\setminus\{ 0\})\big)\rtimes{\mathbb{N}}^{F};
End of MathML
.

Hit id71332

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 56
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/85/f033879.xhtml#id71332
no match at pos:266481(000039%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
CobωX,d=xnn=1nNCobnX,d:πnn+1xn+1=xn for all nNsuperscriptCobωXdsuperscriptsubscriptsubscriptxnn1subscriptnNsuperscriptCobnXdsuperscriptsubscriptπnn1subscriptxn1subscriptxn for all nN
End of MathML
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Hit id72308

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 57
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/26/f010030.xhtml#id72308
no match at pos:302828(000034%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Z01N=i=1NSiZSiiδS1++SN,0,superscriptsubscriptZ01Nsuperscriptsubscripti1NsubscriptsubscriptSisuperscriptsubscriptZsubscriptSiisubscriptδsubscriptS1subscriptSN0
End of MathML
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Hit id73038

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 58
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/75/f029983.xhtml#id73038
no match at pos:300490(000086%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
EN,l-EN,ln=0l~|B|n24m+m1lsubscriptENlsuperscriptsubscriptENln0~l|B|superscriptn24msuperscriptm1l
End of MathML
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Hit id77825

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 59
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033485.xhtml#id77825
no match at pos:362328(000033%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
EN,Z0A:=infΨ,HN,Z0AΨ:Ψ1NC0R3C2,Ψ=1:=subscriptsuperscriptE0NZAinfΨsuperscriptsubscriptHNZ0AΨΨsuperscriptsubscript1NsuperscriptsubscriptC0superscriptR3superscriptC2Ψ1
End of MathML
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Hit id80423

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 60
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/53/f020885.xhtml#id80423
no match at pos:391319(000066%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
×w(ϵ2j=1N-1Zj/N-Zj-1/N1/NZ((j-1)/N)1N)j=1N-1d4Zj/N2π4N-1.
End of MathML
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Hit id82684

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 61
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033485.xhtml#id82684
no match at pos:435339(000039%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
JiHN-LJiJiHN-1i-Zxi+N-12xx-CN1/2xxϱJi JiEN-1+1xiN-121-ζ-Z-CN1/2Z1/3δJi JiEN-1JisubscriptJisubscriptHNLsubscriptJisubscriptJisuperscriptsubscriptHN1iZsubscriptxiN12subscriptxxCsuperscriptN12subscriptxxϱsubscriptJi subscriptJisubscriptEN11subscriptxiN121ζZCsuperscriptN12superscriptZ13δsubscriptJi subscriptJisubscriptEN1subscriptJi
End of MathML
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Hit id82729

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 62
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/207/f082789.xhtml#id82729
no match at pos:458153(000038%) VariableMap:[F, b x 2, mathbb x 7, C x 3, ii x 2, ( x 5, cong x 2, ) x 5, / x 2, k x 4, ,, i x 2, bigotimes, rtimes x 3, 1 x 2, textstyle x 2, tau, \ x 21, _ x 5, ^ x 4, big x 4, = x 2, prod, Z x 7] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for 'infty' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
CFZkCi=1kZ/biiZZki=1kCZ/biiZτZ,CFsuperscriptZkCsuperscriptsubscripti1kZsubscriptbiiZsuperscriptZksuperscriptsubscripti1ksubscriptτCZsubscriptbiiZZC(F)\rtimes{\mathbb{Z}}^{k}\cong C\big(\textstyle{\prod _{{i=1}}^{k}}({\mathbb{Z}}/b_{{ii}}{\mathbb{Z}})\big)\rtimes{\mathbb{Z}}^{k}\cong\textstyle{\bigotimes _{{i=1}}^{k}}\big(C({\mathbb{Z}}/b_{{ii}}{\mathbb{Z}})\rtimes _{\tau}{\mathbb{Z}}\big),
End of MathML
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Hit id82999

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 63
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/214/f085506.xhtml#id82999
no match at pos:446051(000059%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
ZGσq-p=-limNWn=1NZsubscriptGσqpsubscriptNWsuperscriptsubscriptn1N
End of MathML
.

Hit id84029

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 64
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/94/f037557.xhtml#id84029
no match at pos:456501(000035%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
limt+Ntnt=1ZN,ifn0,N.subscripttsuperscriptsubscriptNtnt1subscriptZNifn0N
End of MathML
.

Hit id84313

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 65
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/110/f043670.xhtml#id84313
no match at pos:453673(000036%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
fUd:=1Nd+1xZN,hZNdω0,1dCωfx+ωh1/2d.:=subscriptfsuperscriptUdsuperscript1superscriptNd1subscriptxsubscriptZNhsuperscriptsubscriptZNdsubscriptωsuperscript01dsuperscriptCωfxωh1superscript2d
End of MathML
.

Hit id85868

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 66
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/20/f007937.xhtml#id85868
no match at pos:488583(000092%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
H^*Spp-1,Z1/n,ZpPPH^*NP,Zpsuperscript^HsubscriptSpp1Z1nZpsubscriptPPsuperscript^HsubscriptNPZp
End of MathML
.

Hit id89800

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 67
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/150/f059763.xhtml#id89800
no match at pos:542962(000065%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
vMK,EKvR/ZN×Z/2ZNsubscriptvsubscriptMKEsubscriptKvsuperscriptRZNsuperscriptZ2ZsuperscriptN
End of MathML
.

Hit id94662

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 68
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/218/f087168.xhtml#id94662
no match at pos:621478(000088%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
vUv×K×K×=Z/NZ×subscriptvsubscriptUvsuperscriptsubscriptKsuperscriptKsuperscriptZNZ
End of MathML
.

Hit id95237

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 69
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/122/f048602.xhtml#id95237
no match at pos:637789(000068%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n=1C=Cζ0=C-1/2superscriptsubscriptn1CsuperscriptCζ0superscriptC12
End of MathML
.

Hit id95611

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 70
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/218/f087168.xhtml#id95611
no match at pos:635939(000090%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
U/Z/NZ×1+P2subscriptUsuperscriptZNZ1superscriptsubscriptP2
End of MathML
.

Hit id95961

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 71
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/156/f062224.xhtml#id95961
no match at pos:630464(000069%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
limNn=1N-1dZndZ*n2πiexpiSZ*,Z,subscriptNsuperscriptsubscriptn1N1dZndsuperscriptZn2πiiSsuperscriptZZ
End of MathML
.

Hit id96152

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 72
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/218/f087168.xhtml#id96152
no match at pos:644570(000091%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
vUv×K×K×=Z/NZ×subscriptvsubscriptUvsuperscriptsubscriptKsuperscriptKsuperscriptZNZ
End of MathML
.

Hit id96779

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 73
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/122/f048602.xhtml#id96779
no match at pos:660693(000070%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n=1C=C-1/2superscriptsubscriptn1CsuperscriptC12
End of MathML
.

Hit id98550

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 74
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/218/f087168.xhtml#id98550
no match at pos:681740(000097%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
Z/NZ×=vUv×K×K×superscriptZNZsubscriptvsubscriptUvsuperscriptsubscriptKsuperscriptK
End of MathML
.

Hit idp1009056

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 75
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/168/f066858.xhtml#idp1009056
no match at pos:130446(000010%) VariableMap:[] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 1 occurences for '_' but has only 0 Expects 1 occurences for '^' but has only 0 Expects 1 occurences for '=' but has only 0 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
ZNV;N1,N2=i=1N10dλiλiN2-N1e-NVλiΔΛ2subscriptZNVsubscriptN1subscriptN2superscriptsubscriptproducti1subscriptN1superscriptsubscript0dsubscriptλisuperscriptsubscriptλisubscriptN2subscriptN1superscripteNVsubscriptλiΔsuperscriptΛ2
End of MathML
.

Hit idp135120

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 76
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/16/f006080.xhtml#idp135120
no match at pos:169582(000084%) VariableMap:[ln, n x 3, *, sum, ( x 3, m, ) x 3, ., H, j x 4, jm, , x 8, hat x 2, - x 2, lambda, T, 1, quad, \ x 13, _ x 6, ^, = x 2] Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'N' but has only 0 Expects 1 occurences for '/' but has only 0 Expects 1 occurences for 'infty' but has only 0 Expects 2 occurences for '1' but has only 1 Expects 1 occurences for 'prod' but has only 0 Expects 1 occurences for 'Z' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
H*(j)=-Tln(λj)(n^j-1),n^j=mnjm.superscriptsubscriptHjTsubscriptλjsubscript^nj1subscript^njsubscriptmsubscriptnjmH_{*}^{{(j)}}\,=\,-T\ln(\lambda _{j})(\hat{n}_{j}-1)\,,\quad\hat{n}_{j}\,=\,\sum _{{m}}\, n_{{jm}}\,.
End of MathML
.

Hit id55955

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 77
  • Formulasearchengine score: -9986140
  • Reference to collection: _PREFIX_/27/f010596.xhtml#id55955
found all required tokens in TeX $Z^{{(\beta)}}_{\nu}(m_{1},\ldots,m_{{N_{f}}})=\Bigl(\prod _{{i=1}}^{{N_{f}}}m_{i}\Bigr)^{\nu}\int _{0}^{\infty}\!\!\!\cdots\int _{0}^{\infty}\prod _{{i=1}}^{N}\Bigl(dx_{i}\, x_{i}^{{\beta(\nu+1)/2-1}}{\rm e}^{{-\beta x_{i}}}\prod _{{j=1}}^{{N_{f}}}(x_{i}+m_{j}^{2})\Bigr)\prod _{{i>j}}^{N}|x_{i}-x_{j}|^{\beta}~,$ at pos:37946(8%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.96875 * TOKEN_SCORE[N] + 1.984375 * TOKEN_SCORE[(] + 1.984375 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.75 * TOKEN_SCORE[infty] + 1.984375 * TOKEN_SCORE[1] + 1.9999999850988388 * TOKEN_SCORE[\] + 1.9999990463256836 * TOKEN_SCORE[_] + 1.999755859375 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[=] + 1.9375 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.96875*0.367378648065486+1.984375*0.00418257496311516+1.984375*0.00417601612706465+1.5*0.184871254938806+1.75*0.382802832581921+1.984375*0.0102451205633244+1.9999999850988388*5.92879328325965E-4+1.9999990463256836*0.00257082788077282+1.999755859375*0.00338742677192689+1.9375*2.678806489+1.9375*15.4961284798907+1.5*1.08914121500786 = -9986140.369026188' final score ~ -9986140 reviewer: xxx gave 0
Rendered MathML:
Zνβm1,,mNf=i=1Nfmiν00i=1Ndxixiβν+1/2-1e-βxij=1Nfxi+mj2i>jNxi-xjβ,subscriptsuperscriptZβνsubscriptm1subscriptmsubscriptNfsuperscriptsuperscriptsubscripti1subscriptNfsubscriptmiνsuperscriptsubscript0superscriptsubscript0superscriptsubscripti1Ndsubscriptxisuperscriptsubscriptxiβν121superscripteβsubscriptxisuperscriptsubscriptj1subscriptNfsubscriptxisuperscriptsubscriptmj2superscriptsubscriptijNsuperscriptsubscriptxisubscriptxjβZ^{{(\beta)}}_{\nu}(m_{1},\ldots,m_{{N_{f}}})=\Bigl(\prod _{{i=1}}^{{N_{f}}}m_{i}\Bigr)^{\nu}\int _{0}^{\infty}\!\!\!\cdots\int _{0}^{\infty}\prod _{{i=1}}^{N}\Bigl(dx_{i}\, x_{i}^{{\beta(\nu+1)/2-1}}{\rm e}^{{-\beta x_{i}}}\prod _{{j=1}}^{{N_{f}}}(x_{i}+m_{j}^{2})\Bigr)\prod _{{i>j}}^{N}|x_{i}-x_{j}|^{\beta}~,
End of MathML
.

Hit id87829

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 82
  • Formulasearchengine score: -9986548
  • Reference to collection: _PREFIX_/140/f055940.xhtml#id87829
found all required tokens in TeX $\sum\limits _{{k\in\mathbb{Z}^{\infty}}}\frac{1}{\theta(k)}=\prod\limits _{{i\in\mathbb{N}}}\ \sum\limits _{{\ell\in\mathbb{Z}}}\frac{1}{\gamma^{{|\ell|}}_{{i,\ell}}}\leq\prod\limits _{{i\in\mathbb{N}}}\left\{ 1+2\sum\limits _{{\ell\geq 1}}|\log\mu _{i}|^{{-\ell}}+2\sum\limits _{{\ell\geq 1}}\mu _{i}^{{\sqrt{\ell}}}\right\}.$ at pos:520902(64%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.96875 * TOKEN_SCORE[1] + 1.9999999999999432 * TOKEN_SCORE[\] + 1.998046875 * TOKEN_SCORE[_] + 1.9375 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[=] + 1.75 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.75*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.96875*0.0102451205633244+1.9999999999999432*5.92879328325965E-4+1.998046875*0.00257082788077282+1.9375*0.00338742677192689+1.5*2.678806489+1.75*15.4961284798907+1.75*1.08914121500786 = -9986548.183198035' final score ~ -9986548 reviewer: xxx gave 0
Rendered MathML:
kZ1θk=iNZ1γi,iN1+21logμi-+21μi.subscriptksuperscriptZ1θksubscriptiNsubscriptZ1subscriptsuperscriptγisubscriptiN12subscript1superscriptsubscriptμi2subscript1superscriptsubscriptμi\sum\limits _{{k\in\mathbb{Z}^{\infty}}}\frac{1}{\theta(k)}=\prod\limits _{{i\in\mathbb{N}}}\ \sum\limits _{{\ell\in\mathbb{Z}}}\frac{1}{\gamma^{{|\ell|}}_{{i,\ell}}}\leq\prod\limits _{{i\in\mathbb{N}}}\left\{ 1+2\sum\limits _{{\ell\geq 1}}|\log\mu _{i}|^{{-\ell}}+2\sum\limits _{{\ell\geq 1}}\mu _{i}^{{\sqrt{\ell}}}\right\}.
End of MathML
.

Hit id56549

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 85
  • Formulasearchengine score: -9986852
  • Reference to collection: _PREFIX_/9/f003543.xhtml#id56549
found all required tokens in TeX $Z(N,V,T)=\lim\limits _{{P\to\infty}}(\frac{mP}{2\pi\beta\hbar^{2}})^{{3NP/2}}\prod\limits _{{s=1}}^{P}\int d\{{\bf r}^{{(s)}}\}{\exp}[-\frac{\beta}{P}({\displaystyle\sum\limits _{{k=1}}^{N}}\frac{mP^{2}}{2\hbar^{2}\beta^{2}}({\bf r}_{k}^{{(s)}}-{\bf r}_{k}^{{(s+1)}})^{2}+V_{{pot}}(\{{\bf r}^{{(s)}}\}))]$ at pos:45068(22%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.998046875 * TOKEN_SCORE[(] + 1.998046875 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.875 * TOKEN_SCORE[1] + 1.9999999962747097 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.999755859375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.75*0.367378648065486+1.998046875*0.00418257496311516+1.998046875*0.00417601612706465+1.5*0.184871254938806+1.5*0.382802832581921+1.875*0.0102451205633244+1.9999999962747097*5.92879328325965E-4+1.984375*0.00257082788077282+1.999755859375*0.00338742677192689+1.875*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986852.7783114' final score ~ -9986852 reviewer: xxx gave 0
Rendered MathML:
ZN,V,T=limPmP2πβ23NP/2s=1Pdrsexp-βPk=1NmP222β2rks-rks+12+VpotrsZNVTsubscriptPsuperscriptmP2πβsuperscript23NP2superscriptsubscripts1PdsuperscriptrsβPsuperscriptsubscriptk1NmsuperscriptP22superscript2superscriptβ2superscriptsuperscriptsubscriptrkssuperscriptsubscriptrks12subscriptVpotsuperscriptrsZ(N,V,T)=\lim\limits _{{P\to\infty}}(\frac{mP}{2\pi\beta\hbar^{2}})^{{3NP/2}}\prod\limits _{{s=1}}^{P}\int d\{{\bf r}^{{(s)}}\}{\exp}[-\frac{\beta}{P}({\displaystyle\sum\limits _{{k=1}}^{N}}\frac{mP^{2}}{2\hbar^{2}\beta^{2}}({\bf r}_{k}^{{(s)}}-{\bf r}_{k}^{{(s+1)}})^{2}+V_{{pot}}(\{{\bf r}^{{(s)}}\}))]
End of MathML
.

Hit idp24983200

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 86
  • Formulasearchengine score: -9986863
  • Reference to collection: _PREFIX_/15/f005908.xhtml#idp24983200
found all required tokens in TeX $I_{{e,N_{f};h}}=\sum _{{k\in\mathbb{Z}}}a^{{N_{f}|k|/2}}\int _{{\mathbb{T}}}\prod _{{i=1}}^{{N_{f}}}\frac{(a^{{1/2}}q^{{1/2+|k|/2}}t_{i}^{{-1}}z^{{\pm 1}};q)_{\infty}}{(a^{{-1/2}}q^{{1/2+|k|/2}}t_{i}z^{{\pm 1}};q)_{\infty}}\frac{dz}{2\pi\textup{i}z},$ at pos:717288(63%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.875 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.9921875 * TOKEN_SCORE[/] + 1.75 * TOKEN_SCORE[infty] + 1.99609375 * TOKEN_SCORE[1] + 1.99993896484375 * TOKEN_SCORE[\] + 1.99951171875 * TOKEN_SCORE[_] + 1.998046875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.875*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.9921875*0.184871254938806+1.75*0.382802832581921+1.99609375*0.0102451205633244+1.99993896484375*5.92879328325965E-4+1.99951171875*0.00257082788077282+1.998046875*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986863.081917882' final score ~ -9986863 reviewer: xxx gave 0
Rendered MathML:
Ie,Nf;h=kZaNf|k|/2Ti=1Nf(a1/2q1/2+|k|/2ti-1z±1;q)(a-1/2q1/2+|k|/2tiz±1;q)dz2πiz,subscriptIesubscriptNfhsubscriptkZsuperscriptasubscriptNfk2subscriptTsuperscriptsubscriptproducti1subscriptNfsubscriptsuperscripta12superscriptq12k2superscriptsubscriptti1superscriptzplus-or-minus1qsubscriptsuperscripta12superscriptq12k2subscripttisuperscriptzplus-or-minus1qdz2πizI_{{e,N_{f};h}}=\sum _{{k\in\mathbb{Z}}}a^{{N_{f}|k|/2}}\int _{{\mathbb{T}}}\prod _{{i=1}}^{{N_{f}}}\frac{(a^{{1/2}}q^{{1/2+|k|/2}}t_{i}^{{-1}}z^{{\pm 1}};q)_{\infty}}{(a^{{-1/2}}q^{{1/2+|k|/2}}t_{i}z^{{\pm 1}};q)_{\infty}}\frac{dz}{2\pi\textup{i}z},
End of MathML
.

Hit idp26007872

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 87
  • Formulasearchengine score: -9986863
  • Reference to collection: _PREFIX_/15/f005908.xhtml#idp26007872
found all required tokens in TeX $I_{{e,N_{f};h}}=\sum _{{k\in\mathbb{Z}}}a^{{N_{f}k/2}}\int _{{\mathbb{T}}}\prod _{{i=1}}^{{N_{f}}}\frac{(a^{{1/2}}q^{{1/2+k/2}}t_{i}^{{-1}}z^{{\pm 1}};q)_{\infty}}{(a^{{-1/2}}q^{{1/2+k/2}}t_{i}z^{{\pm 1}};q)_{\infty}}\frac{dz}{2\pi\textup{i}z},$ at pos:856428(75%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.875 * TOKEN_SCORE[N] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.9921875 * TOKEN_SCORE[/] + 1.75 * TOKEN_SCORE[infty] + 1.99609375 * TOKEN_SCORE[1] + 1.99993896484375 * TOKEN_SCORE[\] + 1.99951171875 * TOKEN_SCORE[_] + 1.998046875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.875*0.367378648065486+1.75*0.00418257496311516+1.75*0.00417601612706465+1.9921875*0.184871254938806+1.75*0.382802832581921+1.99609375*0.0102451205633244+1.99993896484375*5.92879328325965E-4+1.99951171875*0.00257082788077282+1.998046875*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986863.081917882' final score ~ -9986863 reviewer: xxx gave 0
Rendered MathML:
Ie,Nf;h=kZaNfk/2Ti=1Nf(a1/2q1/2+k/2ti-1z±1;q)(a-1/2q1/2+k/2tiz±1;q)dz2πiz,subscriptIesubscriptNfhsubscriptkZsuperscriptasubscriptNfk2subscriptTsuperscriptsubscriptproducti1subscriptNfsubscriptsuperscripta12superscriptq12k2superscriptsubscriptti1superscriptzplus-or-minus1qsubscriptsuperscripta12superscriptq12k2subscripttisuperscriptzplus-or-minus1qdz2πizI_{{e,N_{f};h}}=\sum _{{k\in\mathbb{Z}}}a^{{N_{f}k/2}}\int _{{\mathbb{T}}}\prod _{{i=1}}^{{N_{f}}}\frac{(a^{{1/2}}q^{{1/2+k/2}}t_{i}^{{-1}}z^{{\pm 1}};q)_{\infty}}{(a^{{-1/2}}q^{{1/2+k/2}}t_{i}z^{{\pm 1}};q)_{\infty}}\frac{dz}{2\pi\textup{i}z},
End of MathML
.

Hit id105853

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 89
  • Formulasearchengine score: -9986889
  • Reference to collection: _PREFIX_/186/f074192.xhtml#id105853
found all required tokens in TeX $\displaystyle Z_{{\rm Reg}}(R_{{N+1}},R_{0})=\lim _{{\begin{array}[]{c}N\to\infty\\ \delta\to 0\end{array}}}{\cal N}\int\prod^{{N}}_{{n=1}}dR_{n}$ at pos:802229(37%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.9375 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.75 * TOKEN_SCORE[1] + 1.99993896484375 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.5 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.9375*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.75*0.0102451205633244+1.99993896484375*5.92879328325965E-4+1.984375*0.00257082788077282+1.5*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986889.734468626' final score ~ -9986889 reviewer: xxx gave 0
Rendered MathML:
ZRegRN+1,R0=limNδ0NNn=1dRnsubscriptZRegsubscriptRN1subscriptR0subscript→N∞→δ0NsubscriptsuperscriptNn1dsubscriptRn\displaystyle Z_{{\rm Reg}}(R_{{N+1}},R_{0})=\lim _{{\begin{array}[]{c}N\to\infty\\ \delta\to 0\end{array}}}{\cal N}\int\prod^{{N}}_{{n=1}}dR_{n}
End of MathML
.

Hit id56343

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 90
  • Formulasearchengine score: -9986889
  • Reference to collection: _PREFIX_/187/f074464.xhtml#id56343
found all required tokens in TeX $\displaystyle Z_{{\rm Reg}}(R_{{N+1}},R_{0})=\lim _{{\begin{array}[]{c}N\to\infty\\ \delta\to 0\end{array}}}{\cal N}\int\prod^{{N}}_{{n=1}}dR_{n}$ at pos:42545(12%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.9375 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.5 * TOKEN_SCORE[infty] + 1.75 * TOKEN_SCORE[1] + 1.99993896484375 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.5 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.9375*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.5*0.382802832581921+1.75*0.0102451205633244+1.99993896484375*5.92879328325965E-4+1.984375*0.00257082788077282+1.5*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986889.734468626' final score ~ -9986889 reviewer: xxx gave 0
Rendered MathML:
ZRegRN+1,R0=limNδ0NNn=1dRnsubscriptZRegsubscriptRN1subscriptR0subscript→N∞→δ0NsubscriptsuperscriptNn1dsubscriptRn\displaystyle Z_{{\rm Reg}}(R_{{N+1}},R_{0})=\lim _{{\begin{array}[]{c}N\to\infty\\ \delta\to 0\end{array}}}{\cal N}\int\prod^{{N}}_{{n=1}}dR_{n}
End of MathML
.

Hit id55013

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 93
  • Formulasearchengine score: -9986907
  • Reference to collection: _PREFIX_/34/f013566.xhtml#id55013
found all required tokens in TeX $p_{{s}}(M)=\frac{1}{Z_{N}}\prod _{{i=1}}^{N}\frac{F\left(\frac{N-i+1}{N}\right)}{F\left(\frac{i}{N}\right)},$ at pos:26066(15%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.96875 * TOKEN_SCORE[N] + 1.875 * TOKEN_SCORE[(] + 1.875 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.875 * TOKEN_SCORE[1] + 1.998046875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[_] + 1.5 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.96875*0.367378648065486+1.875*0.00418257496311516+1.875*0.00417601612706465+1.0*0.184871254938806+1.0*0.382802832581921+1.875*0.0102451205633244+1.998046875*5.92879328325965E-4+1.875*0.00257082788077282+1.5*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986907.313271414' final score ~ -9986907 reviewer: xxx gave 0
Rendered MathML:
psM=1ZNi=1NFN-i+1NFiN,subscriptpsM1subscriptZNsuperscriptsubscripti1NFNi1NFiNp_{{s}}(M)=\frac{1}{Z_{N}}\prod _{{i=1}}^{N}\frac{F\left(\frac{N-i+1}{N}\right)}{F\left(\frac{i}{N}\right)},
End of MathML
.

Hit idp3955024

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 95
  • Formulasearchengine score: -9986915
  • Reference to collection: _PREFIX_/240/f095899.xhtml#idp3955024
found all required tokens in TeX $dU=\frac{\prod _{{i,j=1}}^{N}d^{2}Z_{{ij}}}{\det(1+ZZ^{\dagger})^{{2N}}}\,.$ at pos:505175(76%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.75 * TOKEN_SCORE[1] + 1.96875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[_] + 1.9375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[=] + 1.5 * TOKEN_SCORE[prod] + 1.5 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.75*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*0.184871254938806+1.0*0.382802832581921+1.75*0.0102451205633244+1.96875*5.92879328325965E-4+1.75*0.00257082788077282+1.9375*0.00338742677192689+1.75*2.678806489+1.5*15.4961284798907+1.5*1.08914121500786 = -9986915.676862894' final score ~ -9986915 reviewer: xxx gave 0
Rendered MathML:
dU=i,j=1Nd2Zijdet1+ZZ2N.dUsuperscriptsubscriptproductij1Nsuperscriptd2subscriptZijsuperscript1ZsuperscriptZ2NdU=\frac{\prod _{{i,j=1}}^{N}d^{2}Z_{{ij}}}{\det(1+ZZ^{\dagger})^{{2N}}}\,.
End of MathML
.

Hit id58146

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 98
  • Formulasearchengine score: -9987721
  • Reference to collection: _PREFIX_/223/f088944.xhtml#id58146
found all required tokens in TeX $NZ=(N_{{1}}Z_{{1}}l_{{1}}+N_{{2}}Z_{{2}}l_{{2}})/l$ at pos:76686(37%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.875 * TOKEN_SCORE[1] + 1.0 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[=] + 1.0 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.5*0.0160883895861106+1.75*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.5*0.184871254938806+1.0*0.382802832581921+1.875*0.0102451205633244+1.0*5.92879328325965E-4+1.984375*0.00257082788077282+1.0*0.00338742677192689+1.5*2.678806489+1.0*15.4961284798907+1.75*1.08914121500786 = -9987721.16804465' final score ~ -9987721 reviewer: xxx gave 0
Rendered MathML:
NZ=N1Z1l1+N2Z2l2/lNZsubscriptN1subscriptZ1subscriptl1subscriptN2subscriptZ2subscriptl2lNZ=(N_{{1}}Z_{{1}}l_{{1}}+N_{{2}}Z_{{2}}l_{{2}})/l
End of MathML
.

Hit idp22391760

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 99
  • Formulasearchengine score: -9987730
  • Reference to collection: _PREFIX_/19/f007289.xhtml#idp22391760
found all required tokens in TeX $A+\sum _{{a\in\mathbb{Z}/N\mathbb{Z}}}B(a)+C=0$ at pos:352450(23%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.0 * TOKEN_SCORE[1] + 1.9375 * TOKEN_SCORE[\] + 1.5 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[=] + 1.0 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.5*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.5*0.184871254938806+1.0*0.382802832581921+1.0*0.0102451205633244+1.9375*5.92879328325965E-4+1.5*0.00257082788077282+1.0*0.00338742677192689+1.5*2.678806489+1.0*15.4961284798907+1.75*1.08914121500786 = -9987730.9156912' final score ~ -9987730 reviewer: xxx gave 0
Rendered MathML:
A+aZ/NZB(a)+C=0AsubscriptaZNZBaC0A+\sum _{{a\in\mathbb{Z}/N\mathbb{Z}}}B(a)+C=0
End of MathML
.

Hit idp23044320

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 100
  • Formulasearchengine score: -9987730
  • Reference to collection: _PREFIX_/19/f007289.xhtml#idp23044320
found all required tokens in TeX $A+\sum _{{a\in\mathbb{Z}/N\mathbb{Z}}}B(a)+C=0$ at pos:433460(28%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_FOUND + 1.75 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[N] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.5 * TOKEN_SCORE[/] + 1.0 * TOKEN_SCORE[infty] + 1.0 * TOKEN_SCORE[1] + 1.9375 * TOKEN_SCORE[\] + 1.5 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[=] + 1.0 * TOKEN_SCORE[prod] + 1.75 * TOKEN_SCORE[Z] =+100.0+-100000.0+1.75*0.0160883895861106+1.5*0.367378648065486+1.5*0.00418257496311516+1.5*0.00417601612706465+1.5*0.184871254938806+1.0*0.382802832581921+1.0*0.0102451205633244+1.9375*5.92879328325965E-4+1.5*0.00257082788077282+1.0*0.00338742677192689+1.5*2.678806489+1.0*15.4961284798907+1.75*1.08914121500786 = -9987730.9156912' final score ~ -9987730 reviewer: xxx gave 0
Rendered MathML:
A+aZ/NZB(a)+C=0AsubscriptaZNZBaC0A+\sum _{{a\in\mathbb{Z}/N\mathbb{Z}}}B(a)+C=0
End of MathML
.

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