Gold 89

Q-Meixner–Pollaczek polynomials

Gold ID: 89
Link: https://sigir21.wmflabs.org/wiki/Q-Meixner–Pollaczek_polynomials#math.145.0
Formula: $P_{n} (x; a ∣ q) = a^{- n} e^{i n ϕ} \frac{a^{2}; q_{n}}{(q; q)_{n}} 3 Φ_{2} (q^{-} n, a e^{i (θ + 2 ϕ)}, a e^{- i θ}; a^{2}, 0 ∣ q; q)$
TeX Source: P_{n}(x;a\mid q) = a^{-n} e^{in\phi} \frac{a^2;q_n}{(q;q)_n} {_3}\Phi_2(q^-n, ae^{i(\theta+2\phi)}, ae^{-i\theta}; a^2, 0 \mid q; q)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Translation: P_{n}(x ; a \mid q) = a^{-n} \expe^{in\phi} \frac{a^2;q_n}{\qmultiPochhammersym{q}{q}{n}}{_3} \Phi_2(q^- n , a \expe^{\iunit(\theta + 2 \phi)} , a \expe^{- \iunit \theta} ; a^2 , 0 \mid q ; q)
Expected (Gold Entry): P_{n}(x ; a \mid q) = a^{-n} \expe^{\iunit n\phi} \frac{\qmultiPochhammersym{a^2}{q}{n}}{\qmultiPochhammersym{q}{q}{n}} \qgenhyperphi{3}{2}@{q^- n , a\expe^{\iunit(\theta + 2 \phi)} , a\expe^{- \iunit \theta}}{a^2, 0}{q}{q}

Translation
Expected (Gold Entry): P[n_, x_, a_, q_] := (a)^(- n)* Exp[I*n*\[Phi]]*Divide[Product[QPochhammer[Part[{(a)^(2)},i],q,n],{i,1,Length[{(a)^(2)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(-)* n , a*Exp[I*(\[Theta]+ 2*\[Phi])], a*Exp[- I*\[Theta]]},{(a)^(2), 0},q,q]