Gold 85

Continuous q-Laguerre polynomials

Gold ID

85

Link

https://sigir21.wmflabs.org/wiki/Continuous_q-Laguerre_polynomials#math.139.0

Formula

$P_{n}^{(\alpha )}(x|q)={\frac {(q^{\alpha }+1;q)_{n}}{(q;q)_{n}}}$

TeX Source

P_{n}^{(\alpha)}(x|q)=\frac{(q^\alpha+1;q)_{n}}{(q;q)_{n}}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

P_{n}^{(\alpha)}(x|q)=\frac{(q^\alpha+1;q)_{n}}{(q;q)_{n}}

Expected (Gold Entry)

P_{n}^{(\alpha)}(x|q) = \frac{\qmultiPochhammersym{q^\alpha+1}{q}{n}}{\qPochhammer{q}{q}{n}} \qgenhyperphi{3}{2}@{q^{-n},q^{\alpha/2+1/4}\expe^{\iunit\theta},q^{\alpha/2+1/4}*\expe^{-\iunit\theta}}{q^{\alpha+1},0}{q}{q}

Mathematica

Translation

Expected (Gold Entry)

P[n_, \[Alpha]_, x_, q_] := Divide[Product[QPochhammer[Part[{(q)^\[Alpha]+ 1},i],q,n],{i,1,Length[{(q)^\[Alpha]+ 1}]}],QPochhammer[q, q, n]]*QHypergeometricPFQ[{(q)^(- n), (q)^(\[Alpha]/2 + 1/4)* Exp[I*\[Theta]], (q)^(\[Alpha]/2 + 1/4)* Exp[- I*\[Theta]]},{(q)^(\[Alpha]+ 1), 0},q,q]

Maple

Translation

Expected (Gold Entry)