Formula:KLS:14.19:25

<< Formula:KLS:14.19:24

formula in Continuous q-Laguerre

Formula:KLS:14.19:26 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(\cos\left(\theta+\phi\right);q^{\frac{1}{2}\alpha+\frac{1}{2}}|q\right)=q^{-(\frac{1}{2}\alpha+\frac{1}{4})n}P^{(\alpha)}_{n}\!\left(\cos\theta|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre

Bibliography

Equation in Section 14.19 of KLS.

URL links

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<< Formula:KLS:14.19:24

formula in Continuous q-Laguerre

Formula:KLS:14.19:26 >>