Gold 1
Bessel function
- Gold ID
- 1
- Link
- https://sigir21.wmflabs.org/wiki/Bessel_function#math.51.18
- Formula
- 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 | ||
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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] 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)