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arXiv:math/0310063 [math.CA]AbstractReferencesReviewsResources

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

S. Sadov

Published 2003-10-06Version 1

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.

Comments: 23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics
Categories: math.CA
Subjects: 33C20, 45H05
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