Gold 90

Q-Laguerre polynomials

Gold ID

90

Link

https://sigir21.wmflabs.org/wiki/Q-Laguerre_polynomials#math.149.0

Formula

$L_n^{(\alpha )}(x;q)=\frac{(q^{\alpha +1};q{)}_n}{(q;q{)}_n}{}_1{\varphi }_1(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x)$

TeX Source

\displaystyle L_n^{(\alpha)}(x;q) = \frac{(q^{\alpha+1};q)_n}{(q;q)_n} {}_1\phi_1(q^{-n};q^{\alpha+1};q,-q^{n+\alpha+1}x)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

\qLaguerrepolyL{\alpha}{n}@{x}{q} = \frac{\qmultiPochhammersym{q^{\alpha+1}}{q}{n}}{\qmultiPochhammersym{q}{q}{n}} \qgenhyperphi{1}{1}@{q^{-n}}{q^{\alpha+1}}{q}{- q^{n+\alpha+1} x}

Expected (Gold Entry)

\qLaguerrepolyL{\alpha}{n}@{x}{q} = \frac{\qmultiPochhammersym{q^{\alpha+1}}{q}{n}}{\qmultiPochhammersym{q}{q}{n}} \qgenhyperphi{1}{1}@{q^{-n}}{q^{\alpha+1}}{q}{- q^{n+\alpha+1} x}

Mathematica

Translation

Expected (Gold Entry)

L[n_, \[Alpha]_, x_, q_] := Divide[Product[QPochhammer[Part[{(q)^(\[Alpha]+ 1)},i],q,n],{i,1,Length[{(q)^(\[Alpha]+ 1)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(- n)},{(q)^(\[Alpha]+ 1)},q,- (q)^(n + \[Alpha]+ 1)* x]

Maple

Translation

Expected (Gold Entry)