Formula:KLS:14.10:83

<< Formula:KLS:14.10:82

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:84 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\uparrow 1}C_{2m}\!\left(x;-q^{\la}\,|\,-q\right)=C^{\frac{1}{2}(\la+1)}_{m}\left(2x^{2}-1\right)+C^{\frac{1}{2}(\la+1)}_{m-1}\left(2x^{2}-1\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}$ : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5

Bibliography

Equation in Section 14.10 of KLS.

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<< Formula:KLS:14.10:82

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:84 >>