Formula:KLS:14.23:02

<< Formula:KLS:14.23:01

formula in q-Charlier

Formula:KLS:14.23:03 >>

${\displaystyle{\displaystyle{\displaystyle C_{n}\!\left(q^{-x};a;q\right)=\left(-a^{-1}q;q\right)_{n}\cdot\qHyperrphis{1}{1}@@{q^{-n}}{-a^{-1}q}{q}{-\frac{q^{n+1-x}}{a}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Charlier polynomial : http://drmf.wmflabs.org/wiki/Definition:qCharlier
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.23 of KLS.

URL links

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<< Formula:KLS:14.23:01

formula in q-Charlier

Formula:KLS:14.23:03 >>