Gold 75

Continuous q-Hahn polynomials

Gold ID: 75
Link: https://sigir21.wmflabs.org/wiki/Continuous_q-Hahn_polynomials#math.127.0
Formula: $p_{n} (x; a, b, c | q) = a^{- n} e^{- i n u} (a b e^{2 i u}, a c, a d; q)_{n} *_{4} Φ_{3} (q^{- n}, a b c d q^{n - 1}, a e^{i (t + 2 u)}, a e^{- i t}; a b e^{2 i u}, a c, a d; q; q)$
TeX Source: p_n(x;a,b,c|q)=a^{-n}e^{-inu}(abe^{2iu},ac,ad;q)_n*_4\Phi_3(q^{-n},abcdq^{n-1},ae^{i{(t+2u)}},ae^{-it};abe^{2iu},ac,ad;q;q)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Translation: p_n(x ; a , b , c|q) = a^{-n} \expe^{- \iunit nu} \qmultiPochhammersym{ab \expe^{2 \iunit u} , ac , ad}{q}{n} *_4 \Phi_3(q^{-n} , abcdq^{n-1} , a \expe^{\iunit{(t+2u)}} , a \expe^{- \iunit t} ; ab \expe^{2 \iunit u} , ac , ad ; q ; q)
Expected (Gold Entry): p_n(x ; a , b , c|q) = a^{-n} \expe^{-\iunit nu} \qmultiPochhammersym{ab\expe^{2\iunit u} , ac , ad}{q}{n} * \qgenhyperphi{4}{3}@{q^{-n} , abcdq^{n-1} , a\expe^{\iunit{(t+2u)}} , a\expe^{-\iunit t}}{ab\expe^{2\iunit u} , ac , ad}{q}{q}

Translation
Expected (Gold Entry): p[n_, x_, a_, b_, c_, q_] := (a)^(- n)* Exp[- I*\[Nu]]*Product[QPochhammer[Part[{a*b*Exp[2*I*u], a*c , a*d},i],q,n],{i,1,Length[{a*b*Exp[2*I*u], a*c , a*d}]}]* QHypergeometricPFQ[{(q)^(- n), a*b*c*d*(q)^(n - 1), a*Exp[I*(t + 2*u)], a*Exp[- I*t]},{a*b*Exp[2*I*u], a*c , a*d},q,q]