Toward symbolic integration of elliptic integrals
type: Item
instance of: scholarly article
title: Toward symbolic integration of elliptic integrals
zbMATH Open document ID: 0976.33014
author: B. C. Carlson
published in: Journal of Symbolic Computation
publication date: 2001-11-11T00:00:00Z
review text: Integrals are considered of the form \(\int_y^x\prod_{i=1}^h(a_i+b_it)^{-1/2} \prod_{j=1}^n(a_j+b_jt)^{m_j} dt\), where \(h=3\) or \(4\), \(n\geq h\), the \(m\)'s are integers, and \(y<x\). A method is proposed by which this type of elliptic integrals can be integrated symbolically, without information regarding limits of integration and branch points of the integrand. The integral is expressed in terms of canonical \(R\)-functions [\textit{B. C. Carlson}, Numer. Algorithms 10, No. 1-2, 13-26 (1995; Zbl 0827.65024)]. Software is available at \url{http://www.neta.com/~cherry} or by e-mail at \url{cherry@neta.com}.
Mathematics Subject Classification ID: 33C75
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33F10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1423187
zbMATH Keywords: elliptic integrals
zbMATH Keywords: symbolic integration
zbMATH Keywords: computation of special functions
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: jsco.1999.0336
OpenAlex ID: W1985406461
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DOI: 10.1006/JSCO.1999.0336
description: scientific article; zbMATH DE number 1423187