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Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
journal contributionposted on 2023-05-16, 10:48 authored by David ElliottDavid Elliott, Venturino, E
Starting with some results of Lyness concerning the Euler-Maclaurin expansion of Cauchy principal value integrals over (0, 1) it is shown how, by the use of sigmoidal transformations good approximations can be found for the Hadamard finite-part integral Finite Part integral sign1 0 (Ï†(x)/(x -c)2)dx, where O < c < 1. The analysis is illustrated by some numerical examples.
Publication titleNumerische Mathematik
Department/SchoolSchool of Natural Sciences
Place of publication175 Fifth Ave, New York, USA, Ny, 10010