Formula:KLS:14.13:06

<< Formula:KLS:14.13:05

formula in q-Meixner

Formula:KLS:14.13:07 >>

${\displaystyle{\displaystyle{\displaystyle M_{n}\!\left(q^{-x};b,c;q\right)=\frac{(-1)^{n}q^{n^{2}}}{\left(bq;q\right)_{n}c^{n}}{\widehat{M}}_{n}\!\left(q^{-x}\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixner
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqMeixner

Bibliography

Equation in Section 14.13 of KLS.

URL links

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<< Formula:KLS:14.13:05

formula in q-Meixner

Formula:KLS:14.13:07 >>