Formula:KLS:14.23:20

<< Formula:KLS:14.23:19

formula in q-Charlier

Formula:KLS:14.23:21 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{N\rightarrow\infty}K_{n}\!\left(q^{-x};a^{-1}q^{-N},N;q\right)=C_{n}\!\left(q^{-x};a;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qKrawtchouk
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Charlier polynomial : http://drmf.wmflabs.org/wiki/Definition:qCharlier

Bibliography

Equation in Section 14.23 of KLS.

URL links

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<< Formula:KLS:14.23:19

formula in q-Charlier

Formula:KLS:14.23:21 >>