Formula:KLS:14.20:21

<< Formula:KLS:14.20:20

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:22 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}p_{n}\!\left((1-q)x;q^{\alpha};q\right)=\frac{L^{\alpha}_{n}\left(x\right)}{L^{\alpha}_{n}\left(0\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:20

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:22 >>