Formula:KLS:14.19:30

<< Formula:KLS:14.19:29

formula in Continuous q-Laguerre

Formula:KLS:14.20:01 >>

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}\!\left(x|q^{2}\right)=q^{n\alpha}P^{(\alpha)}_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1

Bibliography

Equation in Section 14.19 of KLS.

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formula in Continuous q-Laguerre

Formula:KLS:14.20:01 >>