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

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

2003-10-06

arxiv.org/abs/math/0310063v1

Mathematics

Classical Analysis and ODEs

23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics

Scientific paper

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.

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