Formula:KLS:14.03:10

<< Formula:KLS:14.03:09

formula in Continuous dual q-Hahn

Formula:KLS:14.03:13 >>

${\displaystyle{\displaystyle{\displaystyle\normctsdualqHahnptilde{n}@@{x}{a}{b}{c}{q}:=\normctsdualqHahnptilde{n}@{x}{a}{b}{c}{q}=\frac{a^{n}\ctsdualqHahn{n}@{x}{a}{b}{c}{q}}{\qPochhammer{ab,ac}{q}{n}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}}}}$ : normalized continuous dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial ${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}}}}$ : http://drmf.wmflabs.org/wiki/Definition:normctsdualqHahnptilde
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsdualqHahn
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.3 of KLS.

URL links

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formula in Continuous dual q-Hahn

Formula:KLS:14.03:13 >>