Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
The authors present an algorithm based on the use of sigmoidal transformations and the Euler-MacLaurin-expansion to evaluate Hadamard finite-part integrals of the form \(\int^1_0 f(x)/(x- c)^{n+1}dx\), where \(c\in(0,1)\) and \(n\in\mathbb{N}\). Also, the quadrature sums are obtained by differentiating the corresponding results for the Cauchy principal value integral. They appear to be numerically effective for small values of \(n\).
scientific article; zbMATH DE number 1096024