Integration of a class of transcendental Liouvillian functions with error-functions. II
type: Item
instance of: scholarly article
title: Integration of a class of transcendental Liouvillian functions with error-functions. II
zbMATH Open document ID: 0796.12004
author: Paul H. Knowles
published in: Journal of Symbolic Computation
publication date: 1994-09-29T00:00:00Z
review text: The first part of the paper [J. Symb. Comp. 13, 525-543 (1992; Zbl 0759.12001)] described an algorithm which determines whether an element of a certain class of transcendental Liouvillian functions has an erf- elementary integral, i.e. an integral built up from elementary functions and error-functions, and which calculates it in case of existence. Here this algorithm is extended to a much larger class of functions. Due to a somewhat technical restriction in the definition of the admissible differential fields there are some transcendental Liouvillian functions which have erf-elementary integers but which the algorithm cannot handle; an example of such a function is given.
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 502897
zbMATH Keywords: symbolic integration
zbMATH Keywords: algorithm
zbMATH Keywords: transcendental Liouvillian functions
zbMATH Keywords: erf-elementary integral
zbMATH Keywords: elementary functions
zbMATH Keywords: error-functions
zbMATH Keywords: differential fields
reviewed by: Friedrich Schwarz
MaRDI profile type: Publication
full work available at URL: jsco.1993.1042
OpenAlex ID: W4253520793
DOI: 10.1006/JSCO.1993.1042
description: scientific article; zbMATH DE number 502897