Formula:KLS:14.22:26

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formula in q-Bessel

Formula:KLS:14.23:01 >>

${\displaystyle{\displaystyle{\displaystyle\frac{y_{n}\!\left(q^{x};a;q\right)}{\left(q;q\right)_{n}}=L^{(x-n)}_{n}\!\left(aq^{n};q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre

Bibliography

Equation in Section 14.22 of KLS.

URL links

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<< Formula:KLS:14.22:25

formula in q-Bessel

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