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__NOTOC__
__NOTOC__
== Bessel Function ==
== Bessel function ==


; Gold ID : 1
; Gold ID : 1
; Link : https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18
; Link : https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18
; Formula : <math>\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</math>
; Formula : <math>\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</math>
; TeX Source : <syntaxhighlight lang="tex" inline >\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</syntaxhighlight>
; TeX Source : <syntaxhighlight lang="tex" inline>\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}</syntaxhighlight>


{| class="wikitable"
{| class="wikitable"
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=== Semantic LaTeX ===
=== Semantic LaTeX ===


; Translation : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{- (m + \frac{1}{2})}@{x} &= (- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{- (m + \frac{1}{2})}@{x} &= (-1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>
; Translation : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{-(m+\frac{1}{2})}@{x} &=(- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{-(m+\frac{1}{2})}@{x} &=(- 1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{- (m + \frac{1}{2})}@{x} &= (- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{- (m + \frac{1}{2})}@{x} &= (-1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="tex" inline>\begin{align}\BesselJ{- (m + \frac{1}{2})}@{x} &= (- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{- (m + \frac{1}{2})}@{x} &= (-1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}</syntaxhighlight>


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=== Mathematica ===
=== Mathematica ===


; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]\nBesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>
; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ[-(m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]\nBesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>
BesselY[-(m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x] BesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]</syntaxhighlight>




=== Maple ===
=== Maple ===


; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ(- (m +(1)\/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)\/(2), x); BesselY(- (m +(1)\/(2)), x) = (- 1)^(m)* BesselJ(m +(1)\/(2), x)</syntaxhighlight>
; Translation : <syntaxhighlight lang="mathematica" inline>BesselJ(-(m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(-(m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ(- (m +(1)\/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)\/(2), x); BesselY(- (m +(1)\/(2)), x) = (- 1)^(m)* BesselJ(m +(1)\/(2), x)</syntaxhighlight>
; Expected (Gold Entry) : <syntaxhighlight lang="mathematica" inline>BesselJ(- (m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(- (m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)</syntaxhighlight>

Revision as of 11:03, 1 September 2021

Bessel function

Gold ID
1
Link
https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18
Formula
J−(m+12)(x)=(−1)m+1Ym+12(x),Y−(m+12)(x)=(−1)mJm+12(x).
TeX Source
\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}
Translation Results
Semantic LaTeX Mathematica Translation Maple Translations
Yes Yes Yes

Semantic LaTeX

Translation
\begin{align}\BesselJ{-(m+\frac{1}{2})}@{x} &=(- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{-(m+\frac{1}{2})}@{x} &=(- 1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}
Expected (Gold Entry)
\begin{align}\BesselJ{- (m + \frac{1}{2})}@{x} &= (- 1)^{m+1} \BesselY{m+\frac{1}{2}}@{x} , \\ \BesselY{- (m + \frac{1}{2})}@{x} &= (-1)^m \BesselJ{m+\frac{1}{2}}@{x} .\end{align}


Mathematica

Translation
BesselJ[-(m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x] BesselY[-(m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]
Expected (Gold Entry)
BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x] BesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]


Maple

Translation
BesselJ(-(m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(-(m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)
Expected (Gold Entry)
BesselJ(- (m +(1)/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)/(2), x); BesselY(- (m +(1)/(2)), x) = (- 1)^(m)* BesselJ(m +(1)/(2), x)
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