Formula:KLS:14.21:23

<< Formula:KLS:14.21:22

formula in q-Laguerre

Formula:KLS:14.21:24 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{\alpha\rightarrow\infty}L^{(\alpha)}_{n}\!\left(xq^{-\alpha};q\right)=S_{n}\!\left(x;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert

Bibliography

Equation in Section 14.21 of KLS.

URL links

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<< Formula:KLS:14.21:22

formula in q-Laguerre

Formula:KLS:14.21:24 >>