Formula:KLS:14.24:18

<< Formula:KLS:14.24:17

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:19 >>

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

Proof

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Symbols List

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

Bibliography

Equation in Section 14.24 of KLS.

URL links

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<< Formula:KLS:14.24:17

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:19 >>