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Preprints of the Keldysh Institute of Applied Mathematics, 2003, 057, 24 pp.
(Mi ipmp930)
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Coupling of the Legendre polynomials with kernels $|x-y|^\alpha$ and $\ln|x-y|$
S. Y. Sadov
Abstract:
Double integrals that represent matrix elements of the power and logarithmic potentials $|x-y|^\alpha$ and $\ln|x-y|$ in the Legendre polynomial basis are found in a closed form. Several proofs are given, which involve different special functions and identities. In particular, a connection of the new formulae and Whipple's hypergeometric summation formula is shown.
Citation:
S. Y. Sadov, “Coupling of the Legendre polynomials with kernels $|x-y|^\alpha$ and $\ln|x-y|$”, Keldysh Institute preprints, 2003, 057, 24 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp930 https://www.mathnet.ru/eng/ipmp/y2003/p57
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