Formula:KLS:14.22:25

<< Formula:KLS:14.22:24

formula in q-Bessel

Formula:KLS:14.22:26 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\frac{\BesselPoly{n}@{q^{x}}{a(1-q};q)}{(q-1)^{n}}=a^{n}\Charlier{n}@{x}{a}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : Bessel polynomial : http://dlmf.nist.gov/18.34#E1
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : Charlier polynomial : http://dlmf.nist.gov/18.19#T1.t1.r11

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:24

formula in q-Bessel

Formula:KLS:14.22:26 >>