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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
Special functions Legendre functions Gegenbauer polynomials Fourier expansions
2011/7/13
Abstract: We use the recent findings of Cohl [arXiv:1105.2735] and evaluate the principal and the residual values of the integral $\int_{-1}^{1}\mathrm{d}t\:(1-t^{2})^{\lambda-1/2}(x-t)^{-\kappa-1/2}C...