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

2003/10/06 by Sergey Sadov, S. Sadov, Sadov, S.
Mathematics · #33C20 #45H05 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #advanced mathematical theories #math.CA #msc:33C20 #msc:45H05

paper · pdf · doi:10.48550/arxiv.math/0310063

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

arxiv created 2003/10/06 · openalex publication_date 2003/10/06 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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.

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