Formula:KLS:14.21:02

<< Formula:KLS:14.21:01

formula in q-Laguerre

Formula:KLS:14.21:03 >>

${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}\!\left(x;q\right)=\frac{1}{\left(q;q\right)_{n}}\,\qHyperrphis{2}{1}@@{q^{-n},-x}{0}{q}{q^{n+\alpha+1}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.21 of KLS.

URL links

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<< Formula:KLS:14.21:01

formula in q-Laguerre

Formula:KLS:14.21:03 >>