Formula:KLS:14.22:13

<< Formula:KLS:14.22:12

formula in q-Bessel

Formula:KLS:14.22:14 >>

${\displaystyle{\displaystyle{\displaystyle\qderiv{q}\qBesselPoly{n}@{x}{a}{q}=-\frac{q^{-n+1}(1-q^{n})(1+aq^{n})}{1-q}\qBesselPoly{n-1}@{x}{aq^{2}}{q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:12

formula in q-Bessel

Formula:KLS:14.22:14 >>