Formula:KLS:14.11:20

<< Formula:KLS:14.11:19

formula in Big q-Laguerre

Formula:KLS:14.11:21 >>

${\displaystyle{\displaystyle{\displaystyle\left(aqt;q\right)_{\infty}\cdot\qHyperrphis{2}{1}@@{bqx^{-1},0}{bq}{q}{xt}=\sum_{n=0}^{\infty}\frac{\left(aq;q\right)_{n}}{\left(q;q\right)_{n}}P_{n}\!\left(x;a,b;q\right)t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLaguerre

Bibliography

Equation in Section 14.11 of KLS.

URL links

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<< Formula:KLS:14.11:19

formula in Big q-Laguerre

Formula:KLS:14.11:21 >>