Formula:KLS:14.19:26

<< Formula:KLS:14.19:25

formula in Continuous q-Laguerre

Formula:KLS:14.19:27 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{\beta\rightarrow\infty}P^{(\alpha,\beta)}_{n}\!\left(x|q\right)=P^{(\alpha)}_{n}\!\left(x|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre

Bibliography

Equation in Section 14.19 of KLS.

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formula in Continuous q-Laguerre

Formula:KLS:14.19:27 >>