Gold 83

Big q-Laguerre polynomials

Gold ID

83

Link

https://sigir21.wmflabs.org/wiki/Big_q-Laguerre_polynomials#math.137.0

Formula

$P_{n}(x;a,b;q)={\frac {1}{(b^{-1}*q^{-n};q,n)}}*_{2}\Phi _{1}(q^{-n},aqx^{-1};aq|q;{\frac {x}{b}})$

TeX Source

P_n(x;a,b;q)=\frac{1}{(b^{-1}*q^{-n};q,n)}*_2\Phi_1(q^{-n},aqx^{-1};aq|q;\frac{x}{b})

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

P_n(x;a,b;q)=\frac{1}{(b^{-1}*q^{-n};q,n)}*_2\Phi_1(q^{-n},aqx^{-1};aq|q;\frac{x}{b})

Expected (Gold Entry)

P_n(x;a,b;q) =\frac{1}{\qmultiPochhammersym{b^{-1}*q^{-n}}{q}{n}} * \qgenhyperphi{2}{1}@{q^{-n},aqx^{-1}}{aq}{q}{\frac{x}{b}}

Mathematica

Translation

Expected (Gold Entry)

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

Maple

Translation

Expected (Gold Entry)