Formula:KLS:14.20:22

<< Formula:KLS:14.20:21

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:23 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : Charlier polynomial : http://dlmf.nist.gov/18.19#T1.t1.r11

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:21

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:23 >>