Formula:KLS:14.10:64

<< Formula:KLS:14.10:63

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:65 >>

${\displaystyle{\displaystyle{\displaystyle\par P_{n}\!\left(\cos\phi;\beta|q\right)=C_{n}\!\left(\cos\phi;\beta\,|\,q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13

Bibliography

Equation in Section 14.10 of KLS.

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<< Formula:KLS:14.10:63

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:65 >>