Formula:KLS:14.23:08

<< Formula:KLS:14.23:07

formula in q-Charlier

Formula:KLS:14.23:10 >>

${\displaystyle{\displaystyle{\displaystyle q^{n}y(x)=aq^{x}y(x+1)-q^{x}(a-1)y(x)+(1-q^{x})y(x-1)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle y(x)=\qCharlier{n}@{q^{-x}}{a}{q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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:14.23:07

formula in q-Charlier

Formula:KLS:14.23:10 >>