Formula:KLS:14.22:01

<< q-Laguerre

formula in q-Bessel

Formula:KLS:14.22:02 >>

${\displaystyle{\displaystyle{\displaystyle y_{n}\!\left(x;a;q\right)=\qHyperrphis{2}{1}@@{q^{-n},-aq^{n}}{0}{q}{qx}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< q-Laguerre

formula in q-Bessel

Formula:KLS:14.22:02 >>