Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals

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 (φ(x)/(x -c)2)dx, where O < c < 1. The analysis is illustrated by some numerical examples.