Gold 59

Askey–Wilson polynomials

Gold ID

59

Link

https://sigir21.wmflabs.org/wiki/Askey–Wilson_polynomials#math.111.0

Formula

$p_n(x;a,b,c,d|q)=(ab,ac,ad;q{)}_n{a}^{-n}{}_4{\varphi }_3[\begin{array}{cccc}{q}^{-n}& abcd{q}^{n-1}& a{e}^{i\theta }& a{e}^{-i\theta }\\ ab& ac& ad\end{array};q,q]$

TeX Source

p_n(x;a,b,c,d|q) =(ab,ac,ad;q)_na^{-n}\;_{4}\phi_3 \left[\begin{matrix} q^{-n}&abcdq^{n-1}&ae^{i\theta}&ae^{-i\theta} \\ ab&ac&ad \end{matrix} ; q,q \right]

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

p_n(x ; a , b , c , d|q) =(ab , ac , ad ; q)_n a_{4}^{-n} \phi_3 [\begin{matrix}q^{-n} abcdq^{n-1} ae^{\iunit \theta} ae^{- \iunit \theta} ab&ac&ad\end{matrix} ; q , q]

Expected (Gold Entry)

\AskeyWilsonpolyp{n}@{x}{a}{b}{c}{d}{q} = \qmultiPochhammersym{ab , ac , ad}{q}{n} a^{-n} \qgenhyperphi{4}{3}@{q^{-n} , abcdq^{n-1} , a\expe^{\iunit\theta} , a\expe^{-\iunit\theta}}{ab , ac , ad}{q}{q}

Mathematica

Translation

Expected (Gold Entry)

p[n_, x_, a_, b_, c_, d_, q_] := Product[QPochhammer[Part[{a*b , a*c , a*d},i],q,n],{i,1,Length[{a*b , a*c , a*d}]}]*(a)^(- n)* QHypergeometricPFQ[{(q)^(- n), a*b*c*d*(q)^(n - 1), a*Exp[I*\[Theta]], a*Exp[- I*\[Theta]]},{a*b , a*c , a*d},q,q]

Maple

Translation

Expected (Gold Entry)