Formula:KLS:14.10:87

<< Formula:KLS:14.10:86

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:88 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\uparrow 1}C_{n}\!\left(x;-q^{\lambda}\,|\,-q\right)=\mathrm{c}onstS^{(\frac{1}{2}\lambda,\frac{1}{2}\lambda-1)}_{n}\left(x\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle S^{(\alpha,\beta)}_{n}}}}$ : Generalized Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:GenGegenbauer

Bibliography

Equation in Section 14.10 of KLS.

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<< Formula:KLS:14.10:86

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:88 >>