The properties and evaluation of an integral with power singularities
type: Item
instance of: scholarly article
title: The properties and evaluation of an integral with power singularities
zbMATH Open document ID: 0796.65018
author: V. V. Klejza
author: I. V. Klejza
published in: Computational Mathematics and Mathematical Physics
publication date: 1994-03-03T00:00:00Z
review text: The paper is devoted to the computation of integrals of \(f_ \alpha (t):= t^{\alpha-1} (t-1)^{-\alpha} (1-kt)^{\alpha-1}\). The authors present numerical methods for the approximate evaluation of \(\int^{1/k}_ 1 f_ \alpha (u)du\) and \(A_ \alpha (t):=\int^ t_ 1f_ \alpha (u)du\) and give precise estimations of the remainder. The behavior of \(A_ \alpha (t)\) is studied for limit values of \(k\) and \(\alpha\) \((k \to 0,\;k \to 1,\;\alpha \to 0)\).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 486820
zbMATH Keywords: integral with power singularities
zbMATH Keywords: elliptic integrals
zbMATH Keywords: error estimates
zbMATH Keywords: quadrature formula
reviewed by: Borislav D. Bojanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 486820