Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
type: Item
instance of: scholarly article
title: Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
zbMATH Open document ID: 0886.65021
author: E. Venturino
author: David Elliott
published in: Numerische Mathematik
publication date: 1997-12-10T00:00:00Z
review text: 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 \(n\).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65B15
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1096024
zbMATH Keywords: algorithm
zbMATH Keywords: sigmoidal transformations
zbMATH Keywords: Euler-MacLaurin-expansion
zbMATH Keywords: Hadamard finite-part integrals
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
full work available at URL: s002110050295
OpenAlex ID: W2005372492
DOI: 10.1007/S002110050295
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description: scientific article; zbMATH DE number 1096024