Formula:KLS:14.03:10

<< Formula:KLS:14.03:09

formula in Continuous dual q-Hahn

Formula:KLS:14.03:13 >>

${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}\!\left(x\right):={\tilde{p}}_{n}\!\left(x;a,b,c|q\right)=\frac{a^{n}p_{n}\!\left(x;a,b,c|q\right)}{\left(ab,ac;q\right)_{n}}}}}$

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 >>