Formula:KLS:14.04:12

<< Formula:KLS:14.04:11

formula in Continuous q-Hahn

Formula:KLS:14.04:13 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b,c,d;q\right)=2^{n}\left(abcdq^{n-1};q\right)_{n}{\widehat{p}}_{n}\!\left(x\right)}}}$

Proof

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Symbols List

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

Bibliography

Equation in Section 14.4 of KLS.

URL links

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