Coupling of the Legendre polynomials with kernels $|x-y|^\alpha$ and $\ln|x-y|$
Classical Analysis and ODEs
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0310063,
title = {Coupling of the Legendre polynomials with kernels $|x-y|^\alpha$ and $\ln|x-y|$},
author = {S. Sadov},
journal= {arXiv preprint arXiv:math/0310063},
year = {2007}
}
Comments
23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics