Formula:KLS:14.11:25

<< Formula:KLS:14.11:24

formula in Big q-Laguerre

Formula:KLS:14.11:26 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : pseudo Jacobi polynomomal : http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 14.11 of KLS.

URL links

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