Formula:KLS:14.04:24

<< Formula:KLS:14.04:23

formula in Continuous q-Hahn

Formula:KLS:14.04:25 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(\cos\left(\theta+\phi\right);a{\mathrm{e}^{\mathrm{i}\phi}},b{\mathrm{e}^{\mathrm{i}\phi}},c{\mathrm{e}^{-\mathrm{i}\phi}},d{\mathrm{e}^{-\mathrm{i}\phi}}\,|\,q\right)=p_{n}\!\left(\cos\left(\theta+\phi\right);a,b,c,d;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : Askey-Wilson polynomial : http://dlmf.nist.gov/18.28#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqHahn

Bibliography

Equation in Section 14.4 of KLS.

URL links

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formula in Continuous q-Hahn

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