Gold 54

Struve function

Gold ID

54

Link

https://sigir21.wmflabs.org/wiki/Struve_function#math.105.18

Formula

${\mathbf{H}}_{\alpha }(z)=\frac{z^{\alpha +1}}{2^{\alpha }\sqrt{\pi }\mathrm{\Gamma }(\alpha +\frac{3}{2})}{}_1{F}_2(1,\frac{3}{2},\alpha +\frac{3}{2},-\frac{z^2}{4})$

TeX Source

\mathbf{H}_{\alpha}(z) = \frac{z^{\alpha+1}}{2^{\alpha}\sqrt{\pi} \Gamma \left (\alpha+\tfrac{3}{2} \right )} {}_1F_2 \left (1,\tfrac{3}{2}, \alpha+\tfrac{3}{2},-\tfrac{z^2}{4} \right )

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\StruveH{\alpha}@{z} = \frac{z^{\alpha+1}}{2^{\alpha} \sqrt{\cpi} \EulerGamma@{\alpha + \tfrac{3}{2}}}{}_1 F_2(1 , \tfrac{3}{2} , \alpha + \tfrac{3}{2} , - \tfrac{z^2}{4})

Expected (Gold Entry)

\StruveH{\alpha}@{z} = \frac{z^{\alpha+1}}{2^{\alpha} \sqrt{\cpi} \EulerGamma@{\alpha + \tfrac{3}{2}}} \genhyperF{1}{2}@{1}{\tfrac{3}{2}, \alpha + \tfrac{3}{2}}{- \tfrac{z^2}{4}}

Mathematica

Translation

StruveH[\[Alpha], z] == Divide[(z)^(\[Alpha]+ 1),(2)^\[Alpha]*Sqrt[Pi]*Gamma[\[Alpha]+Divide[3,2]]]Subscript[, 1]*Subscript[F, 2][1 ,Divide[3,2], \[Alpha]+Divide[3,2], -Divide[(z)^(2),4]]

Expected (Gold Entry)

StruveH[\[Alpha], z] == Divide[(z)^(\[Alpha]+ 1),(2)^\[Alpha]*Sqrt[Pi]*Gamma[\[Alpha]+Divide[3,2]]]*HypergeometricPFQ[{1}, {Divide[3,2], \[Alpha]+Divide[3,2]}, -Divide[(z)^(2),4]]

Maple

Translation

StruveH(alpha, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))[1]*F[2](1 ,(3)/(2), alpha +(3)/(2), -((z)^(2))/(4))

Expected (Gold Entry)

StruveH(alpha, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))*hypergeom([1], [(3)/(2), alpha +(3)/(2)], -((z)^(2))/(4))