Formula:KLS:14.10:78

<< Formula:KLS:14.10:77

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:79 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1-\beta z^{2}}{1-z^{2}}C_{n}\!\left[q^{\frac{1}{2}}z;\beta\,|\,q\right]+\frac{1-\beta z^{-2}}{1-z^{-2}}C_{n}\!\left[q^{-\frac{1}{2}}z;\beta\,|\,q\right]=(q^{-\frac{1}{2}n}+q^{\frac{1}{2}n}\beta)C_{n}\!\left[z;\beta\,|\,q\right]}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-ultraspherical/Rogers polynomial exponential argument : http://drmf.wmflabs.org/wiki/Definition:ctsqUltrae

Bibliography

Equation in Section 14.10 of KLS.

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formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:79 >>