Formula:KLS:14.04:25

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formula in Continuous q-Hahn

Formula:KLS:14.04:26 >>

${\displaystyle{\displaystyle{\displaystyle\frac{p_{n}\!\left(\cos\left(\theta+\phi\right);a,0,0,a;q\right)}{\left(q;q\right)_{n}}=P_{n}\!\left(\cos\left(\theta+\phi\right);a|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqHahn
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek

Bibliography

Equation in Section 14.4 of KLS.

URL links

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formula in Continuous q-Hahn

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