Formula:KLS:14.23:01

<< q-Bessel

formula in q-Charlier

Formula:KLS:14.23:02 >>

${\displaystyle{\displaystyle{\displaystyle C_{n}\!\left(q^{-x};a;q\right)=\qHyperrphis{2}{1}@@{q^{-n},q^{-x}}{0}{q}{-\frac{q^{n+1}}{a}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.23 of KLS.

URL links

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<< q-Bessel

formula in q-Charlier

Formula:KLS:14.23:02 >>