Formula:KLS:14.21:25

<< Formula:KLS:14.21:24

formula in q-Laguerre

Formula:KLS:14.21:26 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\,\left(q;q\right)_{n}L^{(\alpha)}_{n}\!\left(-q^{-x};q\right)=C_{n}\!\left(x;a\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : Charlier polynomial : http://dlmf.nist.gov/18.19#T1.t1.r11

Bibliography

Equation in Section 14.21 of KLS.

URL links

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<< Formula:KLS:14.21:24

formula in q-Laguerre

Formula:KLS:14.21:26 >>