Formula:KLS:14.04:08

$\displaystyle {\displaystyle \normctsqHahnptilde{n}@@{x}{a}{b}{c}{d}{q}:=\normctsqHahnptilde{n}@{x}{a}{b}{c}{d}{q}=\frac{(a\expe^{\iunit\phi})^n\ctsqHahn{n}@{x}{a}{b}{c}{d}{q}}{\qPochhammer{ab\expe^{2\iunit\phi},ac,ad}{q}{n}} }$

Proof

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Symbols List

$\displaystyle {\displaystyle {\tilde p}_{n}}$  : normalized continuous $\displaystyle {\displaystyle q}$ -Hahn polynomial $\displaystyle {\displaystyle {\tilde p}}$  : http://drmf.wmflabs.org/wiki/Definition:normctsqHahnptilde
$\displaystyle {\displaystyle \mathrm{e}}$  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
$\displaystyle {\displaystyle \mathrm{i}}$  : imaginary unit : http://dlmf.nist.gov/1.9.i
$\displaystyle {\displaystyle p_{n}}$  : continuous $\displaystyle {\displaystyle q}$ -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqHahn
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1