Formula:KLS:14.10:44

<< Formula:KLS:14.10:38

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:45 >>

${\displaystyle{\displaystyle{\displaystyle 2(1-\beta q^{n})xC_{n}\!\left(x;\beta\,|\,q\right)=(1-q^{n+1})C_{n+1}\!\left(x;\beta\,|\,q\right){}+(1-\beta^{2}q^{n-1})C_{n-1}\!\left(x;\beta\,|\,q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : 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:14.10:38

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:45 >>