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

摘要

In this study, we use the recent findings of Cohl [On a generalization of the generating function for Gegenbauer polynomials, arXiv:1105.2735v1] and evaluate two integrals involving the Gegenbauer polynomials: and , both with Re λ−, Re κ, . The results are expressed in terms of the on-the-cut associated Legendre functions and . In addition, we find closed-form representations of the series and , both with Re λ−, Re κ,−1t1,−1x1.View full textDownload full textKeywordsspecial functions, Legendre functions, Gegenbauer polynomials, Fourier expansions MSC 2010:33C55, 33C45, 33C05Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/10652469.2011.642377