Gold 86

Little q-Laguerre polynomials

Gold ID

86

Link

https://sigir21.wmflabs.org/wiki/Little_q-Laguerre_polynomials#math.142.0

Formula

$\displaystyle p_{n}(x;a|q)={}_{2}\phi _{1}(q^{-n},0;aq;q,qx)={\frac {1}{(a^{-1}q^{-n};q)_{n}}}{}_{2}\phi _{0}(q^{-n},x^{-1};;q,x/a)$

TeX Source

\displaystyle p_n(x;a|q) = {}_2\phi_1(q^{-n},0;aq;q,qx) = \frac{1}{(a^{-1}q^{-n};q)_n}{}_2\phi_0(q^{-n},x^{-1};;q,x/a)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

p_n(x ; a|q) = \qgenhyperphi{2}{1}@{q^{-n} , 0}{aq}{q}{qx} = \frac{1}{\qmultiPochhammersym{a^{-1} q^{-n}}{q}{n}}{}_2 \phi_0(q^{-n} , x^{-1} ; ; q , x / a)

Expected (Gold Entry)

p_n(x ; a|q) = \qgenhyperphi{2}{1}@{q^{-n} , 0}{aq}{q}{qx} = \frac{1}{\qmultiPochhammersym{a^{-1} q^{-n}}{q}{n}} \qgenhyperphi{2}{0}@{q^{-n} , x^{-1}}{}{q}{x/a}

Mathematica

Translation

Expected (Gold Entry)

p[n_, x_, a_, q_] := QHypergeometricPFQ[{(q)^(- n), 0},{a*q},q,q*x] == Divide[1,Product[QPochhammer[Part[{(a)^(- 1)* (q)^(- n)},i],q,n],{i,1,Length[{(a)^(- 1)* (q)^(- n)}]}]]*QHypergeometricPFQ[{(q)^(- n), (x)^(- 1)},{},q,x/a]

Maple

Translation

Expected (Gold Entry)