Benchmark

Bessel Function

Gold ID

1

Link

https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18

Formula

${\begin{aligned}J_{-(m+{\frac {1}{2}})}(x)&=(-1)^{m+1}Y_{m+{\frac {1}{2}}}(x),\\Y_{-(m+{\frac {1}{2}})}(x)&=(-1)^{m}J_{m+{\frac {1}{2}}}(x).\end{aligned}}$

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

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]\nBesselY[- (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]\nBesselY[- (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)