Coupling of the Legendre polynomials with kernels $|x-y|^α$ and $\ln|x-y|$

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Double integrals that represent matrix elements of the power and logarithmic potentials in the Legendre polynoiomial basis on [-1,1] are found in a closed form. Several proofs are given, which involve different special functions and identities. A connection of the new formulae and Whipple's hypergeometric summation formula is shown.
23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics

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Classical Analysis and ODEs, 33C20; 45H05

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http://salesiana.dossiersoluciones.com/handle/123456789/68748

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310063
 http://arxiv.org/abs/math/0310063

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arXiv