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arXiv · 1107.2680

Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)

Radosław Szmytkowski
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Abstract

We use the recent findings of Cohl [arXiv:1105.2735] and evaluate two integrals involving the Gegenbauer polynomials: $\int_{-1}^{x}\mathrm{d}t\:(1-t^{2})^{\lambda-1/2}(x-t)^{-\kappa-1/2}C_{n}^{\lambda}(t)$ and $\int_{x}^{1}\mathrm{d}t\:(1-t^{2})^{\lambda-1/2}(t-x)^{-\kappa-1/2}C_{n}^{\lambda}(t)$, both with $\Real\lambda>-1/2$, $\Real\kappa<1/2$, $-1 -1/2$, $\Real\kappa<1/2$, $-1<t<1$, $-1<x<1$.

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Radosław Szmytkowski. 2011-07-13. Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1). https://arxiv.org/abs/1107.2680

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