Gold 76

Continuous dual q-Hahn polynomials

Gold ID

76

Link

https://sigir21.wmflabs.org/wiki/Continuous_dual_q-Hahn_polynomials#math.128.0

Formula

$p_{n}(x;a,b,c\mid q)={\frac {(ab,ac;q)_{n}}{a^{n}}}\cdot {_{3}\Phi _{2}}(q^{-}n,ae^{i\theta },ae^{-i\theta };ab,ac\mid q;q)$

TeX Source

p_n(x;a,b,c\mid q)=\frac{(ab,ac;q)_n}{a^n}\cdot {_3\Phi_2}(q^-n,ae^{i\theta},ae^{-i\theta}; ab, ac \mid q;q)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

p_n(x ; a , b , c \mid q) = \frac{\qmultiPochhammersym{ab , ac}{q}{n}}{a^n} \cdot{_3\Phi_2}(q^- n , ae^{\iunit \theta} , ae^{- \iunit \theta} ; ab , ac \mid q ; q)

Expected (Gold Entry)

p_n(x ; a , b , c \mid q) = \frac{\qmultiPochhammersym{ab , ac}{q}{n}}{a^n} \cdot \qgenhyperphi{3}{2}@{q^{- n} , a\expe^{\iunit \theta} , a\expe^{- \iunit \theta}}{ab , ac}{q}{q}

Mathematica

Translation

Expected (Gold Entry)

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

Maple

Translation

Expected (Gold Entry)