Formula:KLS:14.25:16

<< Formula:KLS:14.25:15

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:17 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{c\rightarrow 0}M_{n}\!\left(x;-ac^{-1},c;q\right)=\left(-\frac{1}{a}\right)^{n}q^{\binomial{n}{2}}V^{(a)}_{n}\!\left(x;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII

Bibliography

Equation in Section 14.25 of KLS.

URL links

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<< Formula:KLS:14.25:15

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:17 >>