Gold 93

Ferrers function

Gold ID

93

Link

https://sigir21.wmflabs.org/wiki/Ferrers_function#math.152.1

Formula

$Q_{v}^{\mu }(x)=\cos(\mu \pi )\left({\frac {1+x}{1-x}}\right)^{\mu /2}{\frac {F(v+1,-v;1-\mu ;1/2-2/x)}{\Gamma (1-\mu )}}$

TeX Source

Q_v^\mu(x)= \cos(\mu\pi)\left(\frac{1+x}{1-x}\right)^{\mu/2}\frac{F(v+1,-v;1-\mu;1/2-2/x)} {\Gamma(1-\mu ) }

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\FerrersQ[\mu]{v}@{x} = \cos(\mu \cpi)(\frac{1+x}{1-x})^{\mu/2} \frac{F(v+1,-v;1-\mu;1/2-2/x)} {\Gamma(1-\mu ) }

Expected (Gold Entry)

\FerrersQ[\mu]{v}@{x} = \cos(\mu \cpi)(\frac{1+x}{1-x})^{\mu/2} \frac{\hyperF@{v+1}{-v}{1-\mu}{1/2-2/x}}{\EulerGamma@{1-\mu}}

Mathematica

Translation

LegendreQ[v, \[Mu], x] == Cos[(\[Mu]*Pi)*]*(Divide[1 + x,1 - x])^(\[Mu]/2)*Divide[F[v + 1 , - v ; 1 - \[Mu]; 1/2 - 2/x],\[CapitalGamma]*(1 - \[Mu])]

Expected (Gold Entry)

LegendreQ[v, \[Mu], x] == Cos[(\[Mu]*Pi)]*(Divide[1 + x,1 - x])^(\[Mu]/2)*Divide[Hypergeometric2F1[v + 1, - v, 1 - \[Mu], 1/2 - 2/x],Gamma[1 - \[Mu]]]

Maple

Translation

LegendreQ(v, mu, x) = cos((mu*Pi)*)*((1 + x)/(1 - x))^(mu/2)*(F(v + 1 , - v ; 1 - mu ; 1/2 - 2/x))/(Gamma*(1 - mu))

Expected (Gold Entry)

LegendreQ(v, mu, x) = cos((mu*Pi))*((1 + x)/(1 - x))^(mu/2)*(hypergeom([v + 1, - v], [1 - mu], 1/2 - 2/x))/(GAMMA(1 - mu))