Coupling of the Legendre Polynomials with Kernels |x-y|α and ln|x-y|.
Abstract:
Double integrals that represent matrix elements of the power and logarithmic potentials |x-y|α 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.
Publication language:russian, pages:24
Research direction:
Mathematical problems and theory of numerical methods
