Formula:KLS:14.13:22

<< Formula:KLS:14.13:21

formula in q-Meixner

Formula:KLS:14.13:23 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{c\rightarrow\infty}M_{n}\!\left(cq^{\alpha}x;q^{\alpha},c;q\right)=\frac{\left(q;q\right)_{n}}{\left(q^{\alpha+1};q\right)_{n}}L^{(\alpha)}_{n}\!\left(x;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre

Bibliography

Equation in Section 14.13 of KLS.

URL links

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<< Formula:KLS:14.13:21

formula in q-Meixner

Formula:KLS:14.13:23 >>