Formula:KLS:14.15:22

<< Formula:KLS:14.15:21

formula in q-Krawtchouk

Formula:KLS:14.15:23 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{N\rightarrow\infty}\qKrawtchouk{n}@{q^{x-N}}{p}{N}{q}=\qBesselPoly{n}@{q^{x}}{p}{q}}}}$

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
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Formula:KLS:14.15:21

formula in q-Krawtchouk

Formula:KLS:14.15:23 >>