Radius of Convergence

Results for NTCIR10-FT-5

Query

Original Query

NTCIR10-FT-5 Full Text Query Radius of Convergence \sum\frac{n!x^{n}}{n^{n}} n ! x n n n n superscript x n superscript n n radius of convergence The open problem at could use a hint.

Compiled by FSE

Token-Filter

  • TeXFilter:[!, n x 4, sum, \ x 2, ^ x 2, x, frac]
  • Presentation-MathML:[!, ∑, n x 4, x]

MathML-Filter

mrow[mo[∑];mfrac[mrow[mrow[mi[n];mi[!]];msup[mi[x];mi[n]]];msup[mi[n];mi[n]]]] apply[sum;apply[divide;apply[times;apply[factorial;ci[n]];apply[csymbol[superscript];ci[x];ci[n]]];apply[csymbol[superscript];ci[n];ci[n]]]]

Word filter

Keywords:[radius, of, convergence] Rendered Presentation-MathML: n!xnnn

Results

Summary

Reviewer score 2

  • Items reviewd: 56
  • Accumulated score: 285244
  • Formulasearchengine found: 18

Reviewer score 0

  • Items reviewd: 44
  • Accumulated score: 465113
  • Formulasearchengine found: 30
.
+++o
200000+0000
5000-2000000183048
<50000381452
05644100
50000000:0 200000:0 10000:48 5000:48

Short result list

Detailed results for reviewer score 2

Hit id56294

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 2
  • Formulasearchengine score: 17982
  • Reference to collection: _PREFIX_/33/f013125.xhtml#id56294
found all required tokens in TeX $W_{0}(z)=\sum _{{n=1}}^{{\infty}}\frac{(-n)^{{n-1}}}{n!}z^{n}\;.$ at pos:41238(8%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9921875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.999755859375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.9921875*10.9765492381723+2.0*0.0833397735003705+1.999755859375*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.875*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17982.57964178934' final score ~ 17982 reviewer: xxx gave 2
Rendered MathML:
W0z=n=1-nn-1n!zn.subscriptW0zsuperscriptsubscriptn1superscriptnn1nsuperscriptznW_{0}(z)=\sum _{{n=1}}^{{\infty}}\frac{(-n)^{{n-1}}}{n!}z^{n}\;.
End of MathML
.

Hit id56960

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 3
  • Formulasearchengine score: 17982
  • Reference to collection: _PREFIX_/33/f013125.xhtml#id56960
found all required tokens in TeX $\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-n)^{{n-1}}}{(n-1)!}z^{{n-1}}\;,$ at pos:50617(10%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9921875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.999755859375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.9921875*10.9765492381723+2.0*0.0833397735003705+1.999755859375*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.875*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17982.581494537244' final score ~ 17982 reviewer: xxx gave 2
Rendered MathML:
n=1-nn-1n-1!zn-1,superscriptsubscriptn1superscriptnn1n1superscriptzn1\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-n)^{{n-1}}}{(n-1)!}z^{{n-1}}\;,
End of MathML
.

Hit id66720

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 4
  • Formulasearchengine score: 17982
  • Reference to collection: _PREFIX_/33/f013125.xhtml#id66720
found all required tokens in TeX $\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-a)^{{n-1}}n^{{n-2}}}{n!}z^{n}\;,$ at pos:196478(39%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9921875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.999755859375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.984375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.9921875*10.9765492381723+2.0*0.0833397735003705+1.999755859375*27.2286129675667+1.5*1.61179106085198+1.984375*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.9375*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17982.706929639142' final score ~ 17982 reviewer: xxx gave 2
Rendered MathML:
n=1-an-1nn-2n!zn,superscriptsubscriptn1superscriptan1superscriptnn2nsuperscriptzn\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-a)^{{n-1}}n^{{n-2}}}{n!}z^{n}\;,
End of MathML
.

Hit id66991

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 5
  • Formulasearchengine score: 17982
  • Reference to collection: _PREFIX_/33/f013125.xhtml#id66991
found all required tokens in TeX $\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-a)^{{n-1}}n^{{n-1}}}{n!}z^{n}\;.$ at pos:200662(40%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9921875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.999755859375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.984375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.9921875*10.9765492381723+2.0*0.0833397735003705+1.999755859375*27.2286129675667+1.5*1.61179106085198+1.984375*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.9375*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17982.706929639142' final score ~ 17982 reviewer: xxx gave 2
Rendered MathML:
n=1-an-1nn-1n!zn.superscriptsubscriptn1superscriptan1superscriptnn1nsuperscriptzn\displaystyle\sum _{{n=1}}^{{\infty}}\frac{(-a)^{{n-1}}n^{{n-1}}}{n!}z^{n}\;.
End of MathML
.

Hit id120382

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 7
  • Formulasearchengine score: 17855
  • Reference to collection: _PREFIX_/36/f014158.xhtml#id120382
found all required tokens in TeX $\frac{ze^{{zx}}}{e^{z}-1}=\sum _{{n=0}}^{\infty}\frac{B_{n}(x)}{n!}z^{n}..........................................(4.5.1.4)$ at pos:981911(43%) Scoringfunction: ' + TeX_HIT_SCORE + 1.875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.9990234375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.875*10.9765492381723+2.0*0.0833397735003705+1.9990234375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.9375*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 17855.36234228458' final score ~ 17855 reviewer: xxx gave 2
Rendered MathML:
zezxez-1=n=0Bnxn!zn4.5.1.4zsuperscriptezxsuperscriptez1superscriptsubscriptn0subscriptBnxnsuperscriptzn4.5.1.4\frac{ze^{{zx}}}{e^{z}-1}=\sum _{{n=0}}^{\infty}\frac{B_{n}(x)}{n!}z^{n}..........................................(4.5.1.4)
End of MathML
.

Hit id55974

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 8
  • Formulasearchengine score: 17688
  • Reference to collection: _PREFIX_/225/f089689.xhtml#id55974
found all required tokens in TeX $1+\sum _{{n\geq 1}}\frac{u^{n}}{n!}\sum _{{\pi\in S_{n}}}\prod _{{i\geq 1}}x_{i}^{{n_{i}(\pi)}}$ at pos:35707(3%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.984375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.75 * TOKEN_SCORE[sum] + 1.998046875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.984375*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.75*0.450727438769192+1.998046875*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.5*0.0366287198730455 = 17688.770884069352' final score ~ 17688 reviewer: xxx gave 2
Rendered MathML:
1+n1unn!πSni1xiniπ1subscriptn1superscriptunnsubscriptπsubscriptSnsubscripti1superscriptsubscriptxisubscriptniπ1+\sum _{{n\geq 1}}\frac{u^{n}}{n!}\sum _{{\pi\in S_{n}}}\prod _{{i\geq 1}}x_{i}^{{n_{i}(\pi)}}
End of MathML
.

Hit id121103

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 9
  • Formulasearchengine score: 17657
  • Reference to collection: _PREFIX_/184/f073229.xhtml#id121103
found all required tokens in TeX $\displaystyle 2\sum _{{n=0}}^{{+\infty}}\frac{J^{n}}{n!(n+2)!}$ at pos:1021435(66%) Scoringfunction: ' + TeX_HIT_SCORE + 1.96875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.875 * WORD_SCORE[ convergence] + 1.75 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.96875*10.9765492381723+2.0*0.0833397735003705+1.875*27.2286129675667+1.75*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.75*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17657.20435979408' final score ~ 17657 reviewer: xxx gave 2
Rendered MathML:
2n=0+Jnn!n+2!2superscriptsubscriptn0superscriptJnnn2\displaystyle 2\sum _{{n=0}}^{{+\infty}}\frac{J^{n}}{n!(n+2)!}
End of MathML
.

Hit idp3898000

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 11
  • Formulasearchengine score: 17549
  • Reference to collection: _PREFIX_/204/f081597.xhtml#idp3898000
found all required tokens in TeX $\sum _{{n\geq 0}}J_{n}^{{\prime}}(t)\frac{x^{n}}{n!}$ at pos:485778(41%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.9375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.9375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.5*0.0366287198730455 = 17549.656457746452' final score ~ 17549 reviewer: xxx gave 2
Rendered MathML:
n0Jn(t)xnn!subscriptn0superscriptsubscriptJntsuperscriptxnn\sum _{{n\geq 0}}J_{n}^{{\prime}}(t)\frac{x^{n}}{n!}
End of MathML
.

Hit id57358

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 13
  • Formulasearchengine score: 17448
  • Reference to collection: _PREFIX_/29/f011524.xhtml#id57358
found all required tokens in TeX $G_{n}\left(\frac{x_{0}}{y}\right)=\sum _{{p=0}}^{\infty}\frac{g_{p}^{n}(x_{0})}{p!}(y-1)^{p}\,;\;\;\;\; g_{p}^{n}(x_{0})=\left[\frac{\partial^{p}}{\partial y^{p}}G_{n}\left(\frac{x_{0}}{y}\right)\right]_{{y=1}}\,,$ at pos:58931(7%) Scoringfunction: ' + TeX_HIT_SCORE + 1.5 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.999755859375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999990463256836 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[x] + 1.9375 * TOKEN_SCORE[frac] =+100.0+1.5*10.9765492381723+2.0*0.0833397735003705+1.999755859375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9999990463256836*5.92879328325965E-4+1.984375*0.00338742677192689+1.9375*0.053601160227971+1.9375*0.0366287198730455 = 17448.787452289303' final score ~ 17448 reviewer: xxx gave 2
Rendered MathML:
Gnx0y=p=0gpnx0p!y-1p;gpnx0=pypGnx0yy=1,subscriptGnsubscriptx0ysuperscriptsubscriptp0superscriptsubscriptgpnsubscriptx0psuperscripty1psuperscriptsubscriptgpnsubscriptx0subscriptsuperscriptpsuperscriptypsubscriptGnsubscriptx0yy1G_{n}\left(\frac{x_{0}}{y}\right)=\sum _{{p=0}}^{\infty}\frac{g_{p}^{n}(x_{0})}{p!}(y-1)^{p}\,;\;\;\;\; g_{p}^{n}(x_{0})=\left[\frac{\partial^{p}}{\partial y^{p}}G_{n}\left(\frac{x_{0}}{y}\right)\right]_{{y=1}}\,,
End of MathML
.

Hit id62240

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 17
  • Formulasearchengine score: 17317
  • Reference to collection: _PREFIX_/223/f089010.xhtml#id62240
found all required tokens in TeX $\displaystyle\frac{x}{e^{x}-1}=1-\frac{x}{2}-\sum^{{\infty}}_{{n=1}}\frac{(-1)^{n}\cdot B_{n}}{(2n)!}x^{{2n}}\,,$ at pos:131512(7%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9999999925494194 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99609375 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[x] + 1.875 * TOKEN_SCORE[frac] =+100.0+1.9999999925494194*10.9765492381723+2.0*0.0833397735003705+1.75*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.99609375*5.92879328325965E-4+1.9375*0.00338742677192689+1.9375*0.053601160227971+1.875*0.0366287198730455 = 17317.52783065936' final score ~ 17317 reviewer: xxx gave 2
Rendered MathML:
xex-1=1-x2-n=1-1nBn2n!x2n,xsuperscriptex11x2subscriptsuperscriptn1superscript1nsubscriptBn2nsuperscriptx2n\displaystyle\frac{x}{e^{x}-1}=1-\frac{x}{2}-\sum^{{\infty}}_{{n=1}}\frac{(-1)^{n}\cdot B_{n}}{(2n)!}x^{{2n}}\,,
End of MathML
.

Hit id59534

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 19
  • Formulasearchengine score: 17040
  • Reference to collection: _PREFIX_/223/f089170.xhtml#id59534
found all required tokens in TeX $e^{x}=\sum _{{n=0}}^{{\infty}}\frac{x^{n}}{n!}.$ at pos:95783(9%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.75*27.2286129675667+1.5*1.61179106085198+1.875*0.06672875812593+1.5*0.450727438769192+1.875*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 17040.08157621084' final score ~ 17040 reviewer: xxx gave 2
Rendered MathML:
ex=n=0xnn!.superscriptexsuperscriptsubscriptn0superscriptxnne^{x}=\sum _{{n=0}}^{{\infty}}\frac{x^{n}}{n!}.
End of MathML
.

Hit idp409984

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 21
  • Formulasearchengine score: 16561
  • Reference to collection: _PREFIX_/19/f007378.xhtml#idp409984
found all required tokens in TeX $W(z)=\sum _{{n=1}}^{\infty}(-n)^{{n-1}}\frac{z^{n}}{n!}$ at pos:45252(4%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9375 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.5 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.9375*10.9765492381723+2.0*0.0833397735003705+1.5*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.875*5.92879328325965E-4+1.875*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 16561.782045327727' final score ~ 16561 reviewer: xxx gave 2
Rendered MathML:
W(z)=n=1(-n)n-1znn!Wzsuperscriptsubscriptn1superscriptnn1superscriptznnW(z)=\sum _{{n=1}}^{\infty}(-n)^{{n-1}}\frac{z^{n}}{n!}
End of MathML
.

Hit id72919

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 22
  • Formulasearchengine score: 16085
  • Reference to collection: _PREFIX_/146/f058233.xhtml#id72919
found all required tokens in TeX $F(\alpha,\beta;\delta;x)=\sum _{{n=0}}^{{\infty}}\frac{(\alpha)_{n}(\beta)_{n}}{n!(\delta)_{n}}x^{n}$ at pos:300608(44%) Scoringfunction: ' + TeX_HIT_SCORE + 1.5 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.5 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.984375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.998046875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.5*10.9765492381723+2.0*0.0833397735003705+1.5*27.2286129675667+1.5*1.61179106085198+1.984375*0.06672875812593+1.5*0.450727438769192+1.998046875*5.92879328325965E-4+1.75*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 16085.647319219577' final score ~ 16085 reviewer: xxx gave 2
Rendered MathML:
Fα,β;δ;x=n=0αnβnn!δnxnFαβδxsuperscriptsubscriptn0subscriptαnsubscriptβnnsubscriptδnsuperscriptxnF(\alpha,\beta;\delta;x)=\sum _{{n=0}}^{{\infty}}\frac{(\alpha)_{n}(\beta)_{n}}{n!(\delta)_{n}}x^{n}
End of MathML
.

Hit idp313680

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 38
  • Formulasearchengine score: 14451
  • Reference to collection: _PREFIX_/132/f052505.xhtml#idp313680
found all required tokens in TeX $\phi(x)=\sum _{{n=0}}^{{\infty}}\frac{m_{n}x^{n}}{n!}=\sum _{{n=0}}^{{\infty}}\mu _{n}x^{n},$ at pos:32442(4%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.5 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9921875 * TOKEN_SCORE[n] + 1.75 * TOKEN_SCORE[sum] + 1.9921875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.5*27.2286129675667+1.5*1.61179106085198+1.9921875*0.06672875812593+1.75*0.450727438769192+1.9921875*5.92879328325965E-4+1.9375*0.00338742677192689+1.875*0.053601160227971+1.5*0.0366287198730455 = 14451.218432669833' final score ~ 14451 reviewer: xxx gave 2
Rendered MathML:
ϕ(x)=n=0mnxnn!=n=0μnxn,ϕxsuperscriptsubscriptn0subscriptmnsuperscriptxnnsuperscriptsubscriptn0subscriptμnsuperscriptxn\phi(x)=\sum _{{n=0}}^{{\infty}}\frac{m_{n}x^{n}}{n!}=\sum _{{n=0}}^{{\infty}}\mu _{n}x^{n},
End of MathML
.

Hit id104124

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 40
  • Formulasearchengine score: 12605
  • Reference to collection: _PREFIX_/193/f076944.xhtml#id104124
found all required tokens in TeX ${\rho}_{0}=\sum _{{s=0}}^{M}{n!\over s!(n-s)!}{(x^{2})^{s}\over(1+x^{2})^{n}}$ at pos:773507(79%) Scoringfunction: ' + TeX_HIT_SCORE + 1.998046875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.875 * TOKEN_SCORE[!] + 1.875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.0 * TOKEN_SCORE[frac] =+100.0+1.998046875*10.9765492381723+2.0*0.0833397735003705+1.875*1.61179106085198+1.875*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.96875*0.00338742677192689+1.75*0.053601160227971+1.0*0.0366287198730455 = 12605.990371977976' final score ~ 12605 reviewer: xxx gave 2
Rendered MathML:
ρ0=s=0Mn!s!n-s!x2s1+x2nsubscriptρ0superscriptsubscripts0Mnsnssuperscriptsuperscriptx2ssuperscript1superscriptx2n{\rho}_{0}=\sum _{{s=0}}^{M}{n!\over s!(n-s)!}{(x^{2})^{s}\over(1+x^{2})^{n}}
End of MathML
.

Hit idp441856

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 45
  • Formulasearchengine score: 10354
  • Reference to collection: _PREFIX_/150/f059749.xhtml#idp441856
found all required tokens in TeX $e_{q}^{x}=1+\sum _{{n=1}}^{\infty}\frac{Q_{{n-1}}x^{n}}{n!},$ at pos:47500(17%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.875*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 10354.595244944796' final score ~ 10354 reviewer: xxx gave 2
Rendered MathML:
eqx=1+n=1Qn-1xnn!,superscriptsubscripteqx1superscriptsubscriptn1subscriptQn1superscriptxnne_{q}^{x}=1+\sum _{{n=1}}^{\infty}\frac{Q_{{n-1}}x^{n}}{n!},
End of MathML
.

Hit idp542480

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 46
  • Formulasearchengine score: 10354
  • Reference to collection: _PREFIX_/150/f059749.xhtml#idp542480
found all required tokens in TeX $\tau _{\epsilon}(x)=\sum _{{n=0}}^{\infty}\frac{T_{n}x^{n}}{n!},$ at pos:59259(21%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.75*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 10354.558460353852' final score ~ 10354 reviewer: xxx gave 2
Rendered MathML:
τϵx=n=0Tnxnn!,subscriptτϵxsuperscriptsubscriptn0subscriptTnsuperscriptxnn\tau _{\epsilon}(x)=\sum _{{n=0}}^{\infty}\frac{T_{n}x^{n}}{n!},
End of MathML
.

Hit id139969

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 48
  • Formulasearchengine score: 10352
  • Reference to collection: _PREFIX_/165/f065993.xhtml#id139969
found all required tokens in TeX $g=\sum _{{n=0}}^{\infty}\frac{n!}{x^{n}}$ at pos:1334854(49%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.5 * TOKEN_SCORE[!] + 1.875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.5*1.61179106085198+1.875*0.06672875812593+1.5*0.450727438769192+1.875*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.5*0.0366287198730455 = 10352.79581836616' final score ~ 10352 reviewer: xxx gave 2
Rendered MathML:
g=n=0n!xngsuperscriptsubscriptn0nsuperscriptxng=\sum _{{n=0}}^{\infty}\frac{n!}{x^{n}}
End of MathML
.

Hit id130527

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 49
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id130527
no match at pos:1160567(000055%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n05n!n!5znsubscriptn05nsuperscriptn5superscriptzn
End of MathML
.

Hit id132449

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 50
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id132449
no match at pos:1190103(000056%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n03n!2n!6znsubscriptn0superscript3n2superscriptn6superscriptzn
End of MathML
.

Hit id132791

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 51
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id132791
no match at pos:1195530(000057%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n02n!4n!n!6znsubscriptn02n4nsuperscriptn6superscriptzn
End of MathML
.

Hit id133155

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 52
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id133155
no match at pos:1201345(000057%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n02n!23n!n!7znsubscriptn0superscript2n23nsuperscriptn7superscriptzn
End of MathML
.

Hit id133563

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 53
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id133563
no match at pos:1207842(000057%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n02n!4n!8znsubscriptn0superscript2n4superscriptn8superscriptzn
End of MathML
.

Hit id135845

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 54
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/182/f072530.xhtml#id135845
no match at pos:1259019(000098%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Ax:=n=0anxnn!:=Axsuperscriptsubscriptn0ansuperscriptxnn
End of MathML
.

Hit id135985

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 55
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/182/f072530.xhtml#id135985
no match at pos:1261224(000098%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Bx:=n=0bnxnn!:=Bxsuperscriptsubscriptn0bnsuperscriptxnn
End of MathML
.

Hit id140600

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 56
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/126/f050253.xhtml#id140600
no match at pos:1334567(000082%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n=0-1n-12n!2n-1n!222nxn,superscriptsubscriptn0superscript1n12n2n1superscriptn2superscript22nsuperscriptxn
End of MathML
.

Hit id166817

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 57
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/74/f029521.xhtml#id166817
found all required tokens in TeX $\frac{x}{e^{x}-1}\quad=\quad\sum _{{n\geq 0}}\frac{B_{n}}{n!}x^{n},\qquad\zeta(1-n)=-\frac{B_{n}}{n},\quad n>1;\qquad\zeta(0)=B_{1}=-1/2$ at pos:1735021(35%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + NaN * WORD_SCORE[of] + 1.9375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.99609375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.999755859375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.875 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+NaN*0.0833397735003705+1.9375*27.2286129675667+1.5*1.61179106085198+1.99609375*0.06672875812593+1.5*0.450727438769192+1.999755859375*5.92879328325965E-4+1.75*0.00338742677192689+1.875*0.053601160227971+1.875*0.0366287198730455 = NaN' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
xex-1=n0Bnn!xn,ζ1-n=-Bnn,n>1;ζ0=B1=-1/2xsuperscriptex1subscriptn0subscriptBnnsuperscriptxnζ1nsubscriptBnnn1ζ0subscriptB112\frac{x}{e^{x}-1}\quad=\quad\sum _{{n\geq 0}}\frac{B_{n}}{n!}x^{n},\qquad\zeta(1-n)=-\frac{B_{n}}{n},\quad n>1;\qquad\zeta(0)=B_{1}=-1/2
End of MathML
.

Hit id191941

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 58
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/210/f083798.xhtml#id191941
found all required tokens in TeX $f(x)=\sum^{{\infty}}_{{n=0}}\frac{f^{{(n)}}(0)}{n!}x^{n}.$ at pos:2108254(84%) Scoringfunction: ' + TeX_HIT_SCORE + NaN * WORD_SCORE[of] + 1.5 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+NaN*0.0833397735003705+1.5*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.875*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = NaN' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
fx=n=0fn0n!xn.fxsubscriptsuperscriptn0superscriptfn0nsuperscriptxnf(x)=\sum^{{\infty}}_{{n=0}}\frac{f^{{(n)}}(0)}{n!}x^{n}.
End of MathML
.

Hit id55314

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 59
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/136/f054089.xhtml#id55314
no match at pos:27813(000001%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Φ0z=n05n!n!5znsubscriptΦ0zsubscriptn05nsuperscriptn5superscriptzn
End of MathML
.

Hit id55892

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 60
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/152/f060642.xhtml#id55892
no match at pos:36002(000009%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
x2+xex-1=n=0Bnxnn!.x2xsuperscriptex1superscriptsubscriptn0subscriptBnsuperscriptxnn
End of MathML
.

Hit id55925

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 61
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/227/f090597.xhtml#id55925
no match at pos:37159(000004%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Fx=n0fnxnn!,Fxsubscriptn0subscriptfnsuperscriptxnn
End of MathML
.

Hit id56617

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 62
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/174/f069240.xhtml#id56617
no match at pos:53032(000017%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ZpK,x=n=0x2nn!2Z2npK.subscriptZpKxsuperscriptsubscriptn0superscriptx2nsuperscriptn2superscriptsubscriptZ2npK
End of MathML
.

Hit id57423

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 63
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/150/f059953.xhtml#id57423
no match at pos:57998(000034%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
cosax=n=0-1nax2n2n!axsubscriptsuperscriptn0superscript1nsuperscriptax2n2n
End of MathML
.

Hit id58031

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 64
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/228/f091096.xhtml#id58031
no match at pos:66137(000019%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Fkz;Ax=n=0zmn+kAnxmn+k!,zΩ,k=0,1,,m-1.subscriptFkzAxsuperscriptsubscriptn0superscriptzmnksuperscriptAnxmnkzΩk01m1.
End of MathML
.

Hit id59719

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 65
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/143/f057017.xhtml#id59719
no match at pos:89632(000012%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
eqx=xnn!.subscripteqxsuperscriptxnn
End of MathML
.

Hit id60133

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 66
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/151/f060354.xhtml#id60133
no match at pos:98826(000043%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n=0Bnxnn!.superscriptsubscriptn0subscriptBnsuperscriptxnn
End of MathML
.

Hit id60196

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 67
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/249/f099551.xhtml#id60196
no match at pos:101627(000023%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Γx=n=0βnxnn!.Γxsuperscriptsubscriptn0subscriptβnsuperscriptxnn
End of MathML
.

Hit id63938

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 68
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/164/f065277.xhtml#id63938
no match at pos:155842(000044%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ϕ2nznn!subscriptϕ2nsuperscriptznn
End of MathML
.

Hit id68310

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 69
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/162/f064560.xhtml#id68310
no match at pos:227655(000094%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
i=1n-1i!n-i!n!superscriptsubscripti1n1inin
End of MathML
.

Hit id69238

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 70
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/164/f065233.xhtml#id69238
no match at pos:235284(000055%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
1-n1n-1n-1xnn!.1subscriptn1superscriptn1n1superscriptxnn
End of MathML
.

Hit id71993

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 71
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/55/f021692.xhtml#id71993
no match at pos:265283(000082%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ALx=aLnxn/n!subscriptALxsubscriptaLnsuperscriptxnn
End of MathML
.

Hit id72245

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 72
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/104/f041515.xhtml#id72245
no match at pos:287390(000058%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
2extet+1=n=0Enxtnn!2superscriptextsuperscriptet1superscriptsubscriptn0subscriptEnxsuperscripttnn
End of MathML
.

Hit id72564

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 73
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/144/f057245.xhtml#id72564
no match at pos:291067(000069%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
En=1-xnn!e-xsubscriptEn1superscriptxnnsuperscriptex
End of MathML
.

Hit id77881

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 74
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/198/f078834.xhtml#id77881
no match at pos:359773(000054%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
h0x=n=0xnn!2subscripth0xsuperscriptsubscriptn0superscriptxnsuperscriptn2
End of MathML
.

Hit id79632

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 75
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/175/f069858.xhtml#id79632
no match at pos:389865(000068%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
exppx=n=0+xnn!subscriptpxsuperscriptsubscriptn0superscriptxnn
End of MathML
.

Hit id81166

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 76
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/164/f065233.xhtml#id81166
no match at pos:412437(000096%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n1n-1n-1xnn!,subscriptn1superscriptn1n1superscriptxnn
End of MathML
.

Hit id83554

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 77
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033423.xhtml#id83554
no match at pos:459520(000054%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Nz2=k=0z2nxn!Nsuperscriptz2superscriptsubscriptk0superscriptz2nsubscriptxn
End of MathML
.

Hit id86175

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 78
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033423.xhtml#id86175
no match at pos:500298(000058%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Fz=k=0znxn!Fzsuperscriptsubscriptk0superscriptznsubscriptxn
End of MathML
.

Hit id88324

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 79
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/198/f078834.xhtml#id88324
no match at pos:512912(000077%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
h0x=n0xnn!2subscripth0xsubscriptn0superscriptxnsuperscriptn2
End of MathML
.

Hit id88444

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 80
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033420.xhtml#id88444
no match at pos:530784(000071%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n=0ψ,Tnψn!znψn=0Tnψn!znsuperscriptsubscriptn0ψsuperscriptTnψnsuperscriptznψsuperscriptsubscriptn0superscriptTnψnsuperscriptzn
End of MathML
.

Hit id89965

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 81
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/45/f017851.xhtml#id89965
no match at pos:526741(000029%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Δ=n1δnn!dndxnΔsubscriptn1subscriptδnnsuperscriptdndsuperscriptxn
End of MathML
.

Hit id91297

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 82
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/125/f049622.xhtml#id91297
no match at pos:569322(000092%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
ϕx=n=0anxnn!ϕxsuperscriptsubscriptn0subscriptansuperscriptxnn
End of MathML
.

Hit id92468

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 83
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/229/f091243.xhtml#id92468
no match at pos:599198(000068%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
Δ=n1δnn!dndxnΔsubscriptn1subscriptδnnsuperscriptdndsuperscriptxn
End of MathML
.

Hit id93082

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 84
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/158/f063021.xhtml#id93082
no match at pos:605220(000072%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
w=n1nn-1xnn!.wsubscriptn1superscriptnn1superscriptxnn
End of MathML
.

Hit id94639

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 85
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/249/f099205.xhtml#id94639
no match at pos:617456(000059%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
n0cnxnn!subscriptn0subscriptcnsuperscriptxnn
End of MathML
.

Hit id94784

  • Reviwer: xxx
  • Reviwer score: 2
  • Formulasearchengine rank: 86
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/249/f099205.xhtml#id94784
no match at pos:619632(000059%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2
Rendered MathML:
gx=n=0cnxnn!gxsuperscriptsubscriptn0subscriptcnsuperscriptxnn
End of MathML
.

Detailed results for reviewer score 0

Hit id84372

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 1
  • Formulasearchengine score: 17987
  • Reference to collection: _PREFIX_/148/f058999.xhtml#id84372
found all required tokens in TeX $\frac{d^{n}}{dx^{n}}\tan\left(\frac{2}{r}\arctan x\right)|_{{x=0}}=\sum _{{k=1,3,5,\ldots,n}}\left(\frac{2}{r}\right)^{k}\frac{2^{{k+1}}(2^{{k+1}}-1)}{(k+1)!}B_{{k+1}}F(n,k),$ at pos:465955(37%) Scoringfunction: ' + TeX_HIT_SCORE + 1.99609375 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.998046875 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.999755859375 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.9375 * TOKEN_SCORE[frac] =+100.0+1.99609375*10.9765492381723+2.0*0.0833397735003705+1.998046875*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.999755859375*5.92879328325965E-4+1.96875*0.00338742677192689+1.75*0.053601160227971+1.9375*0.0366287198730455 = 17987.663543213654' final score ~ 17987 reviewer: xxx gave 0
Rendered MathML:
dndxntan2rarctanxx=0=k=1,3,5,,n2rk2k+12k+1-1k+1!Bk+1Fn,k,superscriptdndsuperscriptxn2rxx0subscriptk135nsuperscript2rksuperscript2k1superscript2k11k1subscriptBk1Fnk\frac{d^{n}}{dx^{n}}\tan\left(\frac{2}{r}\arctan x\right)|_{{x=0}}=\sum _{{k=1,3,5,\ldots,n}}\left(\frac{2}{r}\right)^{k}\frac{2^{{k+1}}(2^{{k+1}}-1)}{(k+1)!}B_{{k+1}}F(n,k),
End of MathML
.

Hit id120145

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 6
  • Formulasearchengine score: 17917
  • Reference to collection: _PREFIX_/36/f014158.xhtml#id120145
found all required tokens in TeX $|B_{n}(x))=|x^{n}+\sum _{{m=0}}^{{n-1}}x^{m}\frac{n!}{m!(n-m)!}B_{{n-m}}).............(4.5.1.4)$ at pos:978381(43%) Scoringfunction: ' + TeX_HIT_SCORE + 1.875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.9990234375 * WORD_SCORE[ convergence] + 1.875 * TOKEN_SCORE[!] + 1.984375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.75 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.875*10.9765492381723+2.0*0.0833397735003705+1.9990234375*27.2286129675667+1.875*1.61179106085198+1.984375*0.06672875812593+1.5*0.450727438769192+1.75*5.92879328325965E-4+1.875*0.00338742677192689+1.875*0.053601160227971+1.5*0.0366287198730455 = 17917.179335727236' final score ~ 17917 reviewer: xxx gave 0
Rendered MathML:
|Bn(x))=|xn+m=0n-1xmn!m!n-m!Bn-m).(4.5.1.4)||B_{n}(x))=|x^{n}+\sum _{{m=0}}^{{n-1}}x^{m}\frac{n!}{m!(n-m)!}B_{{n-m}}).............(4.5.1.4)
End of MathML
.

Hit id125616

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 10
  • Formulasearchengine score: 17616
  • Reference to collection: _PREFIX_/184/f073229.xhtml#id125616
found all required tokens in TeX $\displaystyle\Gamma(\nu+1)\sum _{{n\geqslant\, 0}}\frac{J^{n}}{n!\,\Gamma(n+\nu+1)}$ at pos:1090715(71%) Scoringfunction: ' + TeX_HIT_SCORE + 1.96875 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.875 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9990234375 * TOKEN_SCORE[\] + 1.5 * TOKEN_SCORE[^] + 1.0 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.96875*10.9765492381723+2.0*0.0833397735003705+1.875*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9990234375*5.92879328325965E-4+1.5*0.00338742677192689+1.0*0.053601160227971+1.5*0.0366287198730455 = 17616.828545200915' final score ~ 17616 reviewer: xxx gave 0
Rendered MathML:
Γν+1n 0Jnn!Γn+ν+1Γν1subscriptn 0superscriptJnnΓnν1\displaystyle\Gamma(\nu+1)\sum _{{n\geqslant\, 0}}\frac{J^{n}}{n!\,\Gamma(n+\nu+1)}
End of MathML
.

Hit id57415

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 12
  • Formulasearchengine score: 17508
  • Reference to collection: _PREFIX_/210/f083643.xhtml#id57415
found all required tokens in TeX $L_{n}^{{x^{0}}}=-\frac{1}{2}\sum _{{m\in\rm{Z}}}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$}\alpha _{{m+n}}^{0}\alpha _{{-m}}^{0}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$},L_{n}^{{x^{1}}}=\frac{1}{2}\sum _{{m\in\rm{Z}}}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$}\alpha _{{m+n}}^{1}\alpha _{{-m}}^{1}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$},$ at pos:58551(11%) Scoringfunction: ' + TeX_HIT_SCORE + 1.5 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.9921875 * WORD_SCORE[ convergence] + 1.9375 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.75 * TOKEN_SCORE[sum] + 1.9999999999999432 * TOKEN_SCORE[\] + 1.99609375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.5*10.9765492381723+2.0*0.0833397735003705+1.9921875*27.2286129675667+1.9375*1.61179106085198+1.9375*0.06672875812593+1.75*0.450727438769192+1.9999999999999432*5.92879328325965E-4+1.99609375*0.00338742677192689+1.75*0.053601160227971+1.75*0.0366287198730455 = 17508.276063794074' final score ~ 17508 reviewer: xxx gave 0
Rendered MathML:
Lnx0=-12mZαm+n0α-m0,Lnx1=12mZαm+n1α-m1,superscriptsubscriptLnsuperscriptx012subscriptmZ∘∘superscriptsubscriptαmn0superscriptsubscriptαm0∘∘superscriptsubscriptLnsuperscriptx112subscriptmZ∘∘superscriptsubscriptαmn1superscriptsubscriptαm1∘∘L_{n}^{{x^{0}}}=-\frac{1}{2}\sum _{{m\in\rm{Z}}}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$}\alpha _{{m+n}}^{0}\alpha _{{-m}}^{0}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$},L_{n}^{{x^{1}}}=\frac{1}{2}\sum _{{m\in\rm{Z}}}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$}\alpha _{{m+n}}^{1}\alpha _{{-m}}^{1}\raisebox{-2.0pt}{${\stackrel{\scriptscriptstyle{\circ}}{\scriptscriptstyle{\circ}}}\:\!$},
End of MathML
.

Hit id122323

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 14
  • Formulasearchengine score: 17390
  • Reference to collection: _PREFIX_/223/f089010.xhtml#id122323
found all required tokens in TeX $\displaystyle x_{n}=\frac{1}{(2\pi i)^{n}}\frac{1}{n!}\partial^{n}_{{\rho}}\log\left[\sum^{{\infty}}_{{m=0}}\frac{\Gamma\!(N(m+\rho)+1)}{\Gamma\!(N\rho+1)}\left(\frac{\Gamma\!(\rho+1)}{\Gamma\!(m+\rho+1)}\right)^{N}z^{m}\right]\Biggr|_{{\rho=0}}\,.$ at pos:1060194(57%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9999999925494194 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.96875 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999990686774 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.9375 * TOKEN_SCORE[frac] =+100.0+1.9999999925494194*10.9765492381723+2.0*0.0833397735003705+1.75*27.2286129675667+1.96875*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9999999990686774*5.92879328325965E-4+1.96875*0.00338742677192689+1.5*0.053601160227971+1.9375*0.0366287198730455 = 17390.766705308983' final score ~ 17390 reviewer: xxx gave 0
Rendered MathML:
xn=12πin1n!ρnlogm=0ΓNm+ρ+1ΓNρ+1Γρ+1Γm+ρ+1Nzmρ=0.subscriptxn1superscript2πin1nsubscriptsuperscriptnρsubscriptsuperscriptm0ΓNmρ1ΓNρ1superscriptΓρ1Γmρ1Nsuperscriptzmρ0\displaystyle x_{n}=\frac{1}{(2\pi i)^{n}}\frac{1}{n!}\partial^{n}_{{\rho}}\log\left[\sum^{{\infty}}_{{m=0}}\frac{\Gamma\!(N(m+\rho)+1)}{\Gamma\!(N\rho+1)}\left(\frac{\Gamma\!(\rho+1)}{\Gamma\!(m+\rho+1)}\right)^{N}z^{m}\right]\Biggr|_{{\rho=0}}\,.
End of MathML
.

Hit id74856

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 15
  • Formulasearchengine score: 17390
  • Reference to collection: _PREFIX_/223/f089010.xhtml#id74856
found all required tokens in TeX $\displaystyle x_{n}=\frac{1}{(2\pi i)^{n}}\frac{1}{n!}\partial^{n}_{{\rho}}\log\left[\sum^{{\infty}}_{{m=0}}\frac{\Gamma\!(N(m+\rho)+1)}{\Gamma\!(N\rho+1)}\left(\frac{\Gamma\!(\rho+1)}{\Gamma\!(m+\rho+1)}\right)^{N}z^{m}\right]\Biggr|_{{\rho=0}}\,.$ at pos:324707(17%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9999999925494194 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.96875 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999990686774 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.9375 * TOKEN_SCORE[frac] =+100.0+1.9999999925494194*10.9765492381723+2.0*0.0833397735003705+1.75*27.2286129675667+1.96875*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9999999990686774*5.92879328325965E-4+1.96875*0.00338742677192689+1.5*0.053601160227971+1.9375*0.0366287198730455 = 17390.766705308983' final score ~ 17390 reviewer: xxx gave 0
Rendered MathML:
xn=12πin1n!ρnlogm=0ΓNm+ρ+1ΓNρ+1Γρ+1Γm+ρ+1Nzmρ=0.subscriptxn1superscript2πin1nsubscriptsuperscriptnρsubscriptsuperscriptm0ΓNmρ1ΓNρ1superscriptΓρ1Γmρ1Nsuperscriptzmρ0\displaystyle x_{n}=\frac{1}{(2\pi i)^{n}}\frac{1}{n!}\partial^{n}_{{\rho}}\log\left[\sum^{{\infty}}_{{m=0}}\frac{\Gamma\!(N(m+\rho)+1)}{\Gamma\!(N\rho+1)}\left(\frac{\Gamma\!(\rho+1)}{\Gamma\!(m+\rho+1)}\right)^{N}z^{m}\right]\Biggr|_{{\rho=0}}\,.
End of MathML
.

Hit idp25564704

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 16
  • Formulasearchengine score: 17381
  • Reference to collection: _PREFIX_/14/f005437.xhtml#idp25564704
found all required tokens in TeX $f_{{\beta}}(x)=\sum _{{n=1}}^{{\infty}}\frac{(-1)^{{n+1}}}{n!}\beta/\bar{\beta}(\beta/\bar{\beta}-1)\ldots(\beta/\bar{\beta}-n+1)(f(x))^{n}$ at pos:781340(84%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.875 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99993896484375 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.875*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.99993896484375*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 17381.072227785808' final score ~ 17381 reviewer: xxx gave 0
Rendered MathML:
fβ(x)=n=1(-1)n+1n!β/β¯(β/β¯-1)(β/β¯-n+1)(f(x))nsubscriptfβxsuperscriptsubscriptn1superscript1n1nβ¯ββ¯β1β¯βn1superscriptfxnf_{{\beta}}(x)=\sum _{{n=1}}^{{\infty}}\frac{(-1)^{{n+1}}}{n!}\beta/\bar{\beta}(\beta/\bar{\beta}-1)\ldots(\beta/\bar{\beta}-n+1)(f(x))^{n}
End of MathML
.

Hit id105120

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 18
  • Formulasearchengine score: 17277
  • Reference to collection: _PREFIX_/8/f003138.xhtml#id105120
found all required tokens in TeX $\varphi(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!}\int\lambda^{{n}}\text{d}\mu(\lambda)=\int e^{{x\lambda}}\text{d}\mu(\lambda)$ at pos:786835(63%) Scoringfunction: ' + TeX_HIT_SCORE + 1.5 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.9375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99993896484375 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.5*10.9765492381723+2.0*0.0833397735003705+1.9375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.99993896484375*5.92879328325965E-4+1.9375*0.00338742677192689+1.875*0.053601160227971+1.5*0.0366287198730455 = 17277.31998642982' final score ~ 17277 reviewer: xxx gave 0
Rendered MathML:
φx=n=0xnn!λndμλ=exλdμλφxsuperscriptsubscriptn0superscriptxnnsuperscriptλndμλsuperscriptexλdμλ\varphi(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!}\int\lambda^{{n}}\text{d}\mu(\lambda)=\int e^{{x\lambda}}\text{d}\mu(\lambda)
End of MathML
.

Hit id61474

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 20
  • Formulasearchengine score: 17040
  • Reference to collection: _PREFIX_/193/f076862.xhtml#id61474
found all required tokens in TeX $a^{{-}}_{q}{|{z}\rangle}=z{|{z}\rangle};\qquad{|{z}\rangle}={\mathcal{N}}^{{-1}}\sum _{{n=0}}^{{\infty}}\frac{H_{n}(x;q)}{\sqrt{(q;q)_{{n}}}}\,\,\frac{z^{n}}{\sqrt{[n]_{q}!}},$ at pos:115377(35%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 1.9999999999999996 * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9998779296875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+1.9999999999999996*0.0833397735003705+1.75*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9998779296875*5.92879328325965E-4+1.9375*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 17040.311422481027' final score ~ 17040 reviewer: xxx gave 0
Rendered MathML:
aq-|z=z|z;|z=N-1n=0Hnx;qq;qnznnq!,a^{{-}}_{q}{|{z}\rangle}=z{|{z}\rangle};\qquad{|{z}\rangle}={\mathcal{N}}^{{-1}}\sum _{{n=0}}^{{\infty}}\frac{H_{n}(x;q)}{\sqrt{(q;q)_{{n}}}}\,\,\frac{z^{n}}{\sqrt{[n]_{q}!}},
End of MathML
.

Hit id135169

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 23
  • Formulasearchengine score: 15842
  • Reference to collection: _PREFIX_/137/f054645.xhtml#id135169
found all required tokens in TeX $\partial _{x}\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\langle{:}\omega^{{\otimes n}}{:}_{\lambda},\varphi^{{\otimes n}}\rangle=\varphi(x)\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\langle{:}\omega^{{\otimes n}}{:}_{\lambda},\varphi^{{\otimes n}}\rangle.$ at pos:1257070(76%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.75 * TOKEN_SCORE[!] + 1.99609375 * TOKEN_SCORE[n] + 1.75 * TOKEN_SCORE[sum] + 1.9999999403953552 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.75*1.61179106085198+1.99609375*0.06672875812593+1.75*0.450727438769192+1.9999999403953552*5.92879328325965E-4+1.984375*0.00338742677192689+1.75*0.053601160227971+1.75*0.0366287198730455 = 15842.595791790569' final score ~ 15842 reviewer: xxx gave 0
Rendered MathML:
xn=01n!:ωn:λ,φn=φ(x)n=01n!:ωn:λ,φn.\partial _{x}\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\langle{:}\omega^{{\otimes n}}{:}_{\lambda},\varphi^{{\otimes n}}\rangle=\varphi(x)\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\langle{:}\omega^{{\otimes n}}{:}_{\lambda},\varphi^{{\otimes n}}\rangle.
End of MathML
.

Hit id122110

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 24
  • Formulasearchengine score: 15803
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id122110
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n~n!}{}_{1}F_{1}(-n,\gamma,x^{2})=\frac{\alpha}{2}\frac{\Gamma(\gamma)}{2\pi i}\int\limits _{{c-i\infty}}^{{c+i\infty}}e^{{s}}s^{{-\gamma}}(1-\frac{x^{2}}{s})\ {}_{3}F_{2}(1,1,1+\frac{\alpha}{2};2,2;1-\frac{x^{2}}{s})\ ds.$ at pos:1042523(87%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999403953552 * TOKEN_SCORE[\] + 1.9921875 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.9921875 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9999999403953552*5.92879328325965E-4+1.9921875*0.00338742677192689+1.875*0.053601160227971+1.9921875*0.0366287198730455 = 15803.041114086162' final score ~ 15803 reviewer: xxx gave 0
Rendered MathML:
n=1α2nnn!F11-n,γ,x2=α2Γγ2πic-ic+iess-γ1-x2sF231,1,1+α2;2,2;1-x2sds.superscriptsubscriptn1subscriptα2nnnsubscriptsubscriptF11nγsuperscriptx2α2Γγ2πisuperscriptsubscriptcicisuperscriptessuperscriptsγ1superscriptx2ssubscriptsubscriptF23111α2221superscriptx2sds\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n~n!}{}_{1}F_{1}(-n,\gamma,x^{2})=\frac{\alpha}{2}\frac{\Gamma(\gamma)}{2\pi i}\int\limits _{{c-i\infty}}^{{c+i\infty}}e^{{s}}s^{{-\gamma}}(1-\frac{x^{2}}{s})\ {}_{3}F_{2}(1,1,1+\frac{\alpha}{2};2,2;1-\frac{x^{2}}{s})\ ds.
End of MathML
.

Hit id60318

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 25
  • Formulasearchengine score: 15803
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id60318
found all required tokens in TeX $\psi _{0}^{{(1)}}(x)=-\frac{1}{2\sqrt{2}}\frac{\Gamma(\gamma-\frac{\alpha}{2})}{\Gamma(\gamma)\sqrt{\Gamma(\gamma)}}x^{{\gamma-\frac{1}{2}}}e^{{-\frac{x^{2}}{2}}}\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n,\gamma,x^{2}).$ at pos:100933(8%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999403953552 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[x] + 1.99609375 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9999999403953552*5.92879328325965E-4+1.984375*0.00338742677192689+1.9375*0.053601160227971+1.99609375*0.0366287198730455 = 15803.38778300412' final score ~ 15803 reviewer: xxx gave 0
Rendered MathML:
ψ01x=-122Γγ-α2ΓγΓγxγ-12e-x22n=1α2nn1n!F11-n,γ,x2.superscriptsubscriptψ01x122Γγα2ΓγΓγsuperscriptxγ12superscriptesuperscriptx22superscriptsubscriptn1subscriptα2nn1nsubscriptsubscriptF11nγsuperscriptx2\psi _{0}^{{(1)}}(x)=-\frac{1}{2\sqrt{2}}\frac{\Gamma(\gamma-\frac{\alpha}{2})}{\Gamma(\gamma)\sqrt{\Gamma(\gamma)}}x^{{\gamma-\frac{1}{2}}}e^{{-\frac{x^{2}}{2}}}\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n,\gamma,x^{2}).
End of MathML
.

Hit id97355

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 26
  • Formulasearchengine score: 15803
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id97355
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(3)_{n}}{n~n!}{}_{2}F_{1}(-n;\gamma;x^{2})=\psi(\gamma)-\log x^{2}+\frac{1}{2}\frac{(\gamma-1)(\gamma-2)}{x^{4}}+\frac{\gamma-1}{x^{2}}-\frac{3}{2}$ at pos:657954(55%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.999969482421875 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.9375 * TOKEN_SCORE[x] + 1.96875 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.999969482421875*5.92879328325965E-4+1.96875*0.00338742677192689+1.9375*0.053601160227971+1.96875*0.0366287198730455 = 15803.282331688099' final score ~ 15803 reviewer: xxx gave 0
Rendered MathML:
n=13nnn!F12-n;γ;x2=ψγ-logx2+12γ-1γ-2x4+γ-1x2-32superscriptsubscriptn1subscript3nnnsubscriptsubscriptF12nγsuperscriptx2ψγsuperscriptx212γ1γ2superscriptx4γ1superscriptx232\sum\limits _{{n=1}}^{\infty}\frac{(3)_{n}}{n~n!}{}_{2}F_{1}(-n;\gamma;x^{2})=\psi(\gamma)-\log x^{2}+\frac{1}{2}\frac{(\gamma-1)(\gamma-2)}{x^{4}}+\frac{\gamma-1}{x^{2}}-\frac{3}{2}
End of MathML
.

Hit id170654

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 27
  • Formulasearchengine score: 15802
  • Reference to collection: _PREFIX_/136/f054400.xhtml#id170654
found all required tokens in TeX $\sum _{{n=0}}^{\infty}P_{n}\left(x(y)\right)L^{n}=\sum _{{n=0}}^{\infty}\left(\frac{1}{n!}L^{n}\frac{\mathrm{d}^{n}}{\mathrm{d}y^{n}}\right)P_{0}\left(x(y)\right)=P_{0}\left(x(y+L)\right)\quad.$ at pos:1836715(89%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.99609375 * TOKEN_SCORE[n] + 1.75 * TOKEN_SCORE[sum] + 1.9999923706054688 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.5*1.61179106085198+1.99609375*0.06672875812593+1.75*0.450727438769192+1.9999923706054688*5.92879328325965E-4+1.984375*0.00338742677192689+1.875*0.053601160227971+1.75*0.0366287198730455 = 15802.97102932332' final score ~ 15802 reviewer: xxx gave 0
Rendered MathML:
n=0PnxyLn=n=01n!LndndynP0xy=P0xy+L.superscriptsubscriptn0subscriptPnxysuperscriptLnsuperscriptsubscriptn01nsuperscriptLnsuperscriptdndsuperscriptynsubscriptP0xysubscriptP0xyL\sum _{{n=0}}^{\infty}P_{n}\left(x(y)\right)L^{n}=\sum _{{n=0}}^{\infty}\left(\frac{1}{n!}L^{n}\frac{\mathrm{d}^{n}}{\mathrm{d}y^{n}}\right)P_{0}\left(x(y)\right)=P_{0}\left(x(y+L)\right)\quad.
End of MathML
.

Hit id95344

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 28
  • Formulasearchengine score: 15802
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id95344
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(2)_{n}}{n~n!}{}_{1}F_{1}(-n;\gamma;x^{2})=\psi(\gamma)-\log x^{2}+\frac{\gamma-1}{x^{2}}-1$ at pos:626841(52%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9990234375 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9990234375*5.92879328325965E-4+1.9375*0.00338742677192689+1.875*0.053601160227971+1.75*0.0366287198730455 = 15802.13542939174' final score ~ 15802 reviewer: xxx gave 0
Rendered MathML:
n=12nnn!F11-n;γ;x2=ψγ-logx2+γ-1x2-1superscriptsubscriptn1subscript2nnnsubscriptsubscriptF11nγsuperscriptx2ψγsuperscriptx2γ1superscriptx21\sum\limits _{{n=1}}^{\infty}\frac{(2)_{n}}{n~n!}{}_{1}F_{1}(-n;\gamma;x^{2})=\psi(\gamma)-\log x^{2}+\frac{\gamma-1}{x^{2}}-1
End of MathML
.

Hit id110845

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 29
  • Formulasearchengine score: 15800
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id110845
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n\ n!}{}_{2}F_{1}(-n,b;\gamma;x^{2})$ at pos:868415(72%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9921875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9921875*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 15800.061466342615' final score ~ 15800 reviewer: xxx gave 0
Rendered MathML:
n=112nnn!F12-n,b;γ;x2superscriptsubscriptn1subscript12nnnsubscriptsubscriptF12nbγsuperscriptx2\sum\limits _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n\ n!}{}_{2}F_{1}(-n,b;\gamma;x^{2})
End of MathML
.

Hit id114151

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 30
  • Formulasearchengine score: 15800
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id114151
found all required tokens in TeX $\displaystyle\sum _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n~n!}{}_{1}F_{1}(-n;\gamma;x^{2})=2\log(2)$ at pos:918851(76%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9921875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9921875*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 15800.061466342615' final score ~ 15800 reviewer: xxx gave 0
Rendered MathML:
n=112nnn!F11-n;γ;x2=2log2superscriptsubscriptn1subscript12nnnsubscriptsubscriptF11nγsuperscriptx222\displaystyle\sum _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n~n!}{}_{1}F_{1}(-n;\gamma;x^{2})=2\log(2)
End of MathML
.

Hit id124846

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 31
  • Formulasearchengine score: 15800
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id124846
found all required tokens in TeX $\displaystyle\sum\limits _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n~n!}{}_{1}F_{1}(-n,\gamma,x^{2})$ at pos:1085490(90%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9921875 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.9921875*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 15800.061466342615' final score ~ 15800 reviewer: xxx gave 0
Rendered MathML:
n=112nnn!F11-n,γ,x2superscriptsubscriptn1subscript12nnnsubscriptsubscriptF11nγsuperscriptx2\displaystyle\sum\limits _{{n=1}}^{\infty}\frac{(\frac{1}{2})_{n}}{n~n!}{}_{1}F_{1}(-n,\gamma,x^{2})
End of MathML
.

Hit id54154

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 32
  • Formulasearchengine score: 15800
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id54154
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n,\gamma,x^{2})$ at pos:10592(1%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99609375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.875 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.99609375*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.875*0.0366287198730455 = 15800.519556934518' final score ~ 15800 reviewer: xxx gave 0
Rendered MathML:
n=1α2nn1n!F11-n,γ,x2superscriptsubscriptn1subscriptα2nn1nsubscriptsubscriptF11nγsuperscriptx2\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n,\gamma,x^{2})
End of MathML
.

Hit id55077

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 33
  • Formulasearchengine score: 15800
  • Reference to collection: _PREFIX_/140/f055741.xhtml#id55077
found all required tokens in TeX $\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n;\gamma;x^{2}),\quad\gamma>\frac{\alpha}{2},\alpha=2,4,\dots$ at pos:23098(2%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.9999980926513672 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.96875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99993896484375 * TOKEN_SCORE[\] + 1.75 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.9375 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.9999980926513672*27.2286129675667+1.5*1.61179106085198+1.96875*0.06672875812593+1.5*0.450727438769192+1.99993896484375*5.92879328325965E-4+1.75*0.00338742677192689+1.5*0.053601160227971+1.9375*0.0366287198730455 = 15800.748714408564' final score ~ 15800 reviewer: xxx gave 0
Rendered MathML:
n=1α2nn1n!F11-n;γ;x2,γ>α2,α=2,4,superscriptsubscriptn1subscriptα2nn1nsubscriptsubscriptF11nγsuperscriptx2γα2α24\sum\limits _{{n=1}}^{\infty}\frac{(\frac{\alpha}{2})_{n}}{n}\frac{1}{n!}{}_{1}F_{1}(-n;\gamma;x^{2}),\quad\gamma>\frac{\alpha}{2},\alpha=2,4,\dots
End of MathML
.

Hit id117670

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 34
  • Formulasearchengine score: 15791
  • Reference to collection: _PREFIX_/137/f054645.xhtml#id117670
found all required tokens in TeX $\displaystyle\qquad\leq\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\big|{:}\omega^{{\otimes n}}{:}_{\lambda}\restriction\Lambda^{n}\big|\sup _{{(x_{1},\dots,x_{n})\in X^{n}}}|f^{{\otimes n}}_{k}(x_{1},\dots,x_{n})-\varphi^{{\otimes n}}(x_{1},\dots,x_{n})|$ at pos:986093(60%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9990234375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.999999761581421 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.984375 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.5*1.61179106085198+1.9990234375*0.06672875812593+1.5*0.450727438769192+1.999999761581421*5.92879328325965E-4+1.984375*0.00338742677192689+1.984375*0.053601160227971+1.5*0.0366287198730455 = 15791.392937926312' final score ~ 15791 reviewer: xxx gave 0
Rendered MathML:
n=01n!|:ωn:λΛn|supx1,,xnXn|fkn(x1,,xn)-φn(x1,,xn)|\displaystyle\qquad\leq\sum _{{n=0}}^{\infty}\frac{1}{n!}\,\big|{:}\omega^{{\otimes n}}{:}_{\lambda}\restriction\Lambda^{n}\big|\sup _{{(x_{1},\dots,x_{n})\in X^{n}}}|f^{{\otimes n}}_{k}(x_{1},\dots,x_{n})-\varphi^{{\otimes n}}(x_{1},\dots,x_{n})|
End of MathML
.

Hit id55050

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 35
  • Formulasearchengine score: 15790
  • Reference to collection: _PREFIX_/137/f054645.xhtml#id55050
found all required tokens in TeX $G(x,z){:=}\exp(x\Psi(z))f(z)=\sum _{{n=0}}^{\infty}\frac{P^{{(n)}}(x)}{n!}\, z^{n}$ at pos:24796(2%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.984375 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.984375*5.92879328325965E-4+1.875*0.00338742677192689+1.875*0.053601160227971+1.5*0.0366287198730455 = 15790.358160638183' final score ~ 15790 reviewer: xxx gave 0
Rendered MathML:
Gx,z:=expxΨzfz=n=0Pnxn!zn:=GxzxΨzfzsuperscriptsubscriptn0superscriptPnxnsuperscriptznG(x,z){:=}\exp(x\Psi(z))f(z)=\sum _{{n=0}}^{\infty}\frac{P^{{(n)}}(x)}{n!}\, z^{n}
End of MathML
.

Hit id111805

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 36
  • Formulasearchengine score: 15789
  • Reference to collection: _PREFIX_/137/f054645.xhtml#id111805
found all required tokens in TeX $\displaystyle{\cal G}_{\lambda}(x,u){:=}\sum _{{n=0}}^{\infty}\frac{u^{n}}{n!}\, P^{{(n)}}_{\lambda}(x)$ at pos:893573(54%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.99609375 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.99609375*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 15789.688840915798' final score ~ 15789 reviewer: xxx gave 0
Rendered MathML:
Gλx,u:=n=0unn!Pλnx:=subscriptGλxusuperscriptsubscriptn0superscriptunnsubscriptsuperscriptPnλx\displaystyle{\cal G}_{\lambda}(x,u){:=}\sum _{{n=0}}^{\infty}\frac{u^{n}}{n!}\, P^{{(n)}}_{\lambda}(x)
End of MathML
.

Hit id112221

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 37
  • Formulasearchengine score: 15789
  • Reference to collection: _PREFIX_/137/f054645.xhtml#id112221
found all required tokens in TeX $\displaystyle{\cal G}_{2}(x,u){:=}\sum _{{n=0}}^{\infty}\frac{u^{n}}{n!}\, P^{{(n)}}_{2}(x)$ at pos:900496(55%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.99609375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.984375 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.99609375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.984375*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 15789.688146135337' final score ~ 15789 reviewer: xxx gave 0
Rendered MathML:
G2x,u:=n=0unn!P2nx:=subscriptG2xusuperscriptsubscriptn0superscriptunnsubscriptsuperscriptPn2x\displaystyle{\cal G}_{2}(x,u){:=}\sum _{{n=0}}^{\infty}\frac{u^{n}}{n!}\, P^{{(n)}}_{2}(x)
End of MathML
.

Hit id109294

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 39
  • Formulasearchengine score: 12629
  • Reference to collection: _PREFIX_/6/f002209.xhtml#id109294
found all required tokens in TeX $h_{{ij}}(\eta,{\mathbf{x}})=l_{{{\mathrm{Pl}}}}\frac{\sqrt{16\pi}}{(2\pi)^{{3/2}}}\ \int _{{-\infty}}^{{\infty}}{\mathrm{d}}^{{3}}{\mathbf{n}}\ \frac{1}{\sqrt{2n}}\ \sum _{{s=1}}^{{2}}\ \stackrel{s}{p}_{{ij}}\!\!({\mathbf{n}})\ \left[\stackrel{s}{h}_{{n}}\!\!(\eta)\ \stackrel{s}{c}_{{{\mathbf{n}}}}\!\!(0)\ {\mathrm{e}}^{{{\mathrm{i}}{\mathbf{n\cdot x}}}}+\stackrel{s}{h}_{{n}}^{{\ast}}(\eta)\ \stackrel{s}{c}_{{{\mathbf{n}}}}^{{\dagger}}(0)\ {\mathrm{e}}^{{-{\mathrm{i}}{\mathbf{n\cdot x}}}}\right],$ at pos:879304(76%) Scoringfunction: ' + TeX_HIT_SCORE + 1.999755859375 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.984375 * TOKEN_SCORE[!] + 1.998046875 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999999999998 * TOKEN_SCORE[\] + 1.99609375 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.999755859375*10.9765492381723+2.0*0.0833397735003705+1.984375*1.61179106085198+1.998046875*0.06672875812593+1.5*0.450727438769192+1.9999999999999998*5.92879328325965E-4+1.99609375*0.00338742677192689+1.875*0.053601160227971+1.75*0.0366287198730455 = 12629.746424820201' final score ~ 12629 reviewer: xxx gave 0
Rendered MathML:
hij(η,x)=lPl16π2π3/2-d3n12ns=12psij(n)[hsn(η)csn(0)einx+hsn(η)csn(0)e-inx],h_{{ij}}(\eta,{\mathbf{x}})=l_{{{\mathrm{Pl}}}}\frac{\sqrt{16\pi}}{(2\pi)^{{3/2}}}\ \int _{{-\infty}}^{{\infty}}{\mathrm{d}}^{{3}}{\mathbf{n}}\ \frac{1}{\sqrt{2n}}\ \sum _{{s=1}}^{{2}}\ \stackrel{s}{p}_{{ij}}\!\!({\mathbf{n}})\ \left[\stackrel{s}{h}_{{n}}\!\!(\eta)\ \stackrel{s}{c}_{{{\mathbf{n}}}}\!\!(0)\ {\mathrm{e}}^{{{\mathrm{i}}{\mathbf{n\cdot x}}}}+\stackrel{s}{h}_{{n}}^{{\ast}}(\eta)\ \stackrel{s}{c}_{{{\mathbf{n}}}}^{{\dagger}}(0)\ {\mathrm{e}}^{{-{\mathrm{i}}{\mathbf{n\cdot x}}}}\right],
End of MathML
.

Hit id55148

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 41
  • Formulasearchengine score: 12549
  • Reference to collection: _PREFIX_/140/f055727.xhtml#id55148
found all required tokens in TeX $\displaystyle=\sum _{{n=0}}^{{\infty}}\left(\frac{i}{2m\omega r^{{2}}}\right)^{{n}}\frac{1}{n!}\underset{n}{\underbrace{\left\{\cdots\left\{\left\{ x_{{k}},j^{{2}}\right\},j^{{2}}\right\},\cdots,j^{{2}}\right\}}}$ at pos:23109(6%) Scoringfunction: ' + TeX_HIT_SCORE + 1.9999999962747097 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999999403953552 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[^] + 1.5 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.9999999962747097*10.9765492381723+2.0*0.0833397735003705+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9999999403953552*5.92879328325965E-4+1.984375*0.00338742677192689+1.5*0.053601160227971+1.75*0.0366287198730455 = 12549.52523844969' final score ~ 12549 reviewer: xxx gave 0
Rendered MathML:
=n=0i2mωr2n1n!xk,j2,j2,,j2nsuperscriptsubscriptn0superscripti2mωsuperscriptr2n1nnsubscriptxksuperscriptj2superscriptj2superscriptj2\displaystyle=\sum _{{n=0}}^{{\infty}}\left(\frac{i}{2m\omega r^{{2}}}\right)^{{n}}\frac{1}{n!}\underset{n}{\underbrace{\left\{\cdots\left\{\left\{ x_{{k}},j^{{2}}\right\},j^{{2}}\right\},\cdots,j^{{2}}\right\}}}
End of MathML
.

Hit id65924

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 42
  • Formulasearchengine score: 12315
  • Reference to collection: _PREFIX_/9/f003244.xhtml#id65924
found all required tokens in TeX $N(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!\;([f(n)]!)^{2}}\;,$ at pos:186925(25%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.75*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 12315.791696389953' final score ~ 12315 reviewer: xxx gave 0
Rendered MathML:
Nx=n=0xnn!fn!2,Nxsuperscriptsubscriptn0superscriptxnnsuperscriptfn2N(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!\;([f(n)]!)^{2}}\;,
End of MathML
.

Hit id81453

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 43
  • Formulasearchengine score: 12315
  • Reference to collection: _PREFIX_/72/f028800.xhtml#id81453
found all required tokens in TeX $N(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!\;([f(n)]!)^{2}}\;.$ at pos:412249(91%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + 2.0 * WORD_SCORE[of] + 1.75 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.96875 * TOKEN_SCORE[\] + 1.875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+2.0*0.0833397735003705+1.75*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.96875*5.92879328325965E-4+1.875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 12315.791696389953' final score ~ 12315 reviewer: xxx gave 0
Rendered MathML:
Nx=n=0xnn!fn!2.Nxsuperscriptsubscriptn0superscriptxnnsuperscriptfn2N(x)=\sum _{{n=0}}^{{\infty}}\frac{x^{{n}}}{n!\;([f(n)]!)^{2}}\;.
End of MathML
.

Hit idp2450160

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 44
  • Formulasearchengine score: 10431
  • Reference to collection: _PREFIX_/18/f006841.xhtml#idp2450160
found all required tokens in TeX $\sum(B(n+1)-B(n))\dfrac{x^{n}}{n!}=\sum B(n+1)\dfrac{x^{n}}{n!}-\sum B(n)\dfrac{x^{n}}{n!}=B^{{\prime}}(x)-B(x)$ at pos:313116(22%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.875 * TOKEN_SCORE[!] + 1.9990234375 * TOKEN_SCORE[n] + 1.875 * TOKEN_SCORE[sum] + 1.9921875 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.96875 * TOKEN_SCORE[x] + 1.0 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.875*1.61179106085198+1.9990234375*0.06672875812593+1.875*0.450727438769192+1.9921875*5.92879328325965E-4+1.9375*0.00338742677192689+1.96875*0.053601160227971+1.0*0.0366287198730455 = 10431.719435546884' final score ~ 10431 reviewer: xxx gave 0
Rendered MathML:
(B(n+1)-B(n))xnn!=B(n+1)xnn!-B(n)xnn!=B(x)-B(x)Bn1BnsuperscriptxnnBn1superscriptxnnBnsuperscriptxnnsuperscriptBxBx\sum(B(n+1)-B(n))\dfrac{x^{n}}{n!}=\sum B(n+1)\dfrac{x^{n}}{n!}-\sum B(n)\dfrac{x^{n}}{n!}=B^{{\prime}}(x)-B(x)
End of MathML
.

Hit idp20648976

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 47
  • Formulasearchengine score: 10354
  • Reference to collection: _PREFIX_/128/f050988.xhtml#idp20648976
found all required tokens in TeX $f_{a}(x)=\sum _{{n}}\frac{\mathrm{pl}(n,an)}{n!}x^{n}\,$ at pos:133878(8%) Scoringfunction: ' + TeX_HIT_SCORE + 2.0 * WORD_SCORE[of] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9375 * TOKEN_SCORE[\] + 1.5 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+2.0*0.0833397735003705+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9375*5.92879328325965E-4+1.5*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = 10354.47192193665' final score ~ 10354 reviewer: xxx gave 0
Rendered MathML:
fa(x)=npl(n,an)n!xnsubscriptfaxsubscriptnplnannsuperscriptxnf_{a}(x)=\sum _{{n}}\frac{\mathrm{pl}(n,an)}{n!}x^{n}\,
End of MathML
.

Hit id112646

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 87
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/74/f029521.xhtml#id112646
found all required tokens in TeX $\sum _{{n_{1},...,n_{m}\geq 0}}\frac{t_{1}^{{n_{1}}}\cdot...\cdot t_{1}^{{n_{m}}}}{(n_{1})!\cdot...\cdot(n_{m})!}\cdot\int...\int _{{0<s_{1}<...<s_{m}<1}}\frac{(-\log s_{1})^{{n_{1}}}\cdot...\cdot(-\log s_{m})^{{n_{m}}}}{(x_{1}-s_{1})\cdot...\cdot(x_{m}-s_{m})}ds_{1}...ds_{m}$ at pos:901246(18%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + NaN * WORD_SCORE[of] + 1.9375 * WORD_SCORE[ convergence] + 1.75 * TOKEN_SCORE[!] + 1.99609375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999923706054688 * TOKEN_SCORE[\] + 1.9375 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.75 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+NaN*0.0833397735003705+1.9375*27.2286129675667+1.75*1.61179106085198+1.99609375*0.06672875812593+1.5*0.450727438769192+1.9999923706054688*5.92879328325965E-4+1.9375*0.00338742677192689+1.75*0.053601160227971+1.75*0.0366287198730455 = NaN' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n1,,nm0t1n1t1nmn1!nm!0<s1<<sm<1-logs1n1-logsmnmx1-s1xm-smds1dsmsubscriptsubscriptn1subscriptnm0superscriptsubscriptt1subscriptn1superscriptsubscriptt1subscriptnmsubscriptn1subscriptnmsubscript0subscripts1subscriptsm1superscriptsubscripts1subscriptn1superscriptsubscriptsmsubscriptnmsubscriptx1subscripts1subscriptxmsubscriptsmdsubscripts1dsubscriptsm\sum _{{n_{1},...,n_{m}\geq 0}}\frac{t_{1}^{{n_{1}}}\cdot...\cdot t_{1}^{{n_{m}}}}{(n_{1})!\cdot...\cdot(n_{m})!}\cdot\int...\int _{{0<s_{1}<...<s_{m}<1}}\frac{(-\log s_{1})^{{n_{1}}}\cdot...\cdot(-\log s_{m})^{{n_{m}}}}{(x_{1}-s_{1})\cdot...\cdot(x_{m}-s_{m})}ds_{1}...ds_{m}
End of MathML
.

Hit id123894

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 88
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/246/f098329.xhtml#id123894
no match at pos:1067063(000087%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
1+xn=m=0nn!xmm!n-m!,superscript1xnsuperscriptsubscriptm0nnsuperscriptxmmnm
End of MathML
.

Hit id134350

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 89
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/74/f029521.xhtml#id134350
found all required tokens in TeX $\sum _{{n\geq 0}}t_{0}^{n}\cdot\int _{0}^{{a_{{m+1}}}}\frac{(\log x)^{n}}{n!}\omega _{1}\circ...\circ\omega _{k}=\int _{0}^{{a_{{m+1}}}}e^{{t_{0}\cdot\log x}}\cdot\omega _{1}\circ...\circ\omega _{k}=$ at pos:1238759(25%) Scoringfunction: ' + TeX_HIT_SCORE + 1.75 * WORD_SCORE[radius] + NaN * WORD_SCORE[of] + 1.9375 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9999961853027344 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.75 * TOKEN_SCORE[x] + 1.5 * TOKEN_SCORE[frac] =+100.0+1.75*10.9765492381723+NaN*0.0833397735003705+1.9375*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9999961853027344*5.92879328325965E-4+1.96875*0.00338742677192689+1.75*0.053601160227971+1.5*0.0366287198730455 = NaN' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n0t0n0am+1logxnn!ω1ωk=0am+1et0logxω1ωk=subscriptn0superscriptsubscriptt0nsuperscriptsubscript0subscriptam1superscriptxnnsubscriptω1subscriptωksuperscriptsubscript0subscriptam1superscriptesubscriptt0xsubscriptω1subscriptωk\sum _{{n\geq 0}}t_{0}^{n}\cdot\int _{0}^{{a_{{m+1}}}}\frac{(\log x)^{n}}{n!}\omega _{1}\circ...\circ\omega _{k}=\int _{0}^{{a_{{m+1}}}}e^{{t_{0}\cdot\log x}}\cdot\omega _{1}\circ...\circ\omega _{k}=
End of MathML
.

Hit id190311

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 90
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/238/f095149.xhtml#id190311
found all required tokens in TeX ${\cal A}[H]=\frac{1}{(4\pi)^{{\frac{d}{2}}}}\sum\limits _{{n=0}}^{{\frac{d}{2}}}\frac{(m^{2})^{{\frac{d}{2}-n}}}{(\frac{d}{2}-n)!}\int d^{d}x\sqrt{g}\; a_{n}(x,x).$ at pos:2119446(45%) Scoringfunction: ' + TeX_HIT_SCORE + 1.96875 * WORD_SCORE[radius] + NaN * WORD_SCORE[of] + 1.75 * WORD_SCORE[ convergence] + 1.5 * TOKEN_SCORE[!] + 1.9375 * TOKEN_SCORE[n] + 1.5 * TOKEN_SCORE[sum] + 1.9998779296875 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[^] + 1.875 * TOKEN_SCORE[x] + 1.984375 * TOKEN_SCORE[frac] =+100.0+1.96875*10.9765492381723+NaN*0.0833397735003705+1.75*27.2286129675667+1.5*1.61179106085198+1.9375*0.06672875812593+1.5*0.450727438769192+1.9998779296875*5.92879328325965E-4+1.96875*0.00338742677192689+1.875*0.053601160227971+1.984375*0.0366287198730455 = NaN' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
AH=14πd2n=0d2m2d2-nd2-n!ddxganx,x.AH1superscript4πd2superscriptsubscriptn0d2superscriptsuperscriptm2d2nd2nsuperscriptddxgsubscriptanxx{\cal A}[H]=\frac{1}{(4\pi)^{{\frac{d}{2}}}}\sum\limits _{{n=0}}^{{\frac{d}{2}}}\frac{(m^{2})^{{\frac{d}{2}-n}}}{(\frac{d}{2}-n)!}\int d^{d}x\sqrt{g}\; a_{n}(x,x).
End of MathML
.

Hit id53609

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 91
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/229/f091395.xhtml#id53609
no match at pos:4216(000002%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
0=n=1xn-1n!dndxnsubscript0superscriptsubscriptn1superscriptxn1nsuperscriptdndsuperscriptxn
End of MathML
.

Hit id61804

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 92
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/55/f021882.xhtml#id61804
no match at pos:123942(000024%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
ηWFϕx=nann!ϕx2n,subscriptηWFϕxsubscriptnsubscriptannϕsuperscriptx2n
End of MathML
.

Hit id62077

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 93
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/180/f071706.xhtml#id62077
no match at pos:141513(000052%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
-1n2n-3!!2nn!xnsuperscript1n2n3superscript2nnsuperscriptxn
End of MathML
.

Hit id69854

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 94
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/242/f096710.xhtml#id69854
no match at pos:256611(000037%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
-1n2n-3!!2nn!xnsuperscript1n2n3superscript2nnsuperscriptxn
End of MathML
.

Hit id79081

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 95
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/180/f071701.xhtml#id79081
no match at pos:394101(000089%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
x02n=2n!22nλnn!.superscriptsubscriptx02n2nsuperscript22nsuperscriptλnn
End of MathML
.

Hit id83247

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 96
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/250/f099618.xhtml#id83247
no match at pos:473721(000026%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n1n!nn=1.subscriptn1nnn1.
End of MathML
.

Hit id87539

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 97
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/84/f033420.xhtml#id87539
no match at pos:517583(000069%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
n=0Tnψn!znsuperscriptsubscriptn0superscriptTnψnsuperscriptzn
End of MathML
.

Hit id88961

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 98
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/103/f041131.xhtml#id88961
no match at pos:521390(000029%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
fBx=xex-1=n=0Bnxnn!subscriptfBxxsuperscriptex1superscriptsubscriptn0subscriptBnsuperscriptxnn
End of MathML
.

Hit id89854

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 99
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/193/f077106.xhtml#id89854
no match at pos:536079(000070%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
sn!npsn1-pk-sdSnknp!n1-p!sssubscriptsnsuperscriptnpssuperscriptn1pkssubscriptdSsuperscriptnknpn1pss
End of MathML
.

Hit id97180

  • Reviwer: xxx
  • Reviwer score: 0
  • Formulasearchengine rank: 100
  • Formulasearchengine score: 0
  • Reference to collection: _PREFIX_/249/f099205.xhtml#id97180
no match at pos:654723(000063%) VariableMap:[] Expects 1 occurences for '!' but has only 0 Expects 4 occurences for 'n' but has only 0 Expects 1 occurences for 'sum' but has only 0 Expects 2 occurences for '\' but has only 0 Expects 2 occurences for '^' but has only 0 Expects 1 occurences for 'x' but has only 0 Expects 1 occurences for 'frac' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0
Rendered MathML:
fx+1=n0nf1xnn!.fx1subscriptn0superscriptnf1superscriptxnn
End of MathML
.

Tags: