Formula:KLS:14.25:19

<< Formula:KLS:14.25:18

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:20 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\frac{V^{(a(1-q))}_{n}\!\left(q^{-x};q\right)}{(q-1)^{n}}=a^{n}C_{n}\!\left(x;a\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : Charlier polynomial : http://dlmf.nist.gov/18.19#T1.t1.r11

Bibliography

Equation in Section 14.25 of KLS.

URL links

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<< Formula:KLS:14.25:18

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:20 >>