Integration in finite terms with special functions: the error function
type: Item
instance of: scholarly article
title: Integration in finite terms with special functions: the error function
zbMATH Open document ID: 0586.68030
DOI: 10.1016/S0747-7171(85)80037-7
author: G. W. Cherry
published in: Journal of Symbolic Computation
publication date: 1985-01-01T00:00:00Z
review text: A decision procedure for integrating a class of transcendental elementary functions in terms of elementary functions and error functions is described. The procedure consists of three mutually exclusive cases. In the first two cases a generalized procedure for completing squares is used to limit the error functions which can appear in the integral to a finite number. This reduces the problem to the solution of a differential equation and we use a result of \textit{R. H. Risch} [Trans. Am. Math. Soc. 139, 167-189 (1969; Zbl 0184.067)] to solve it. The third case can be reduced to the determination of what we have termed \(\Sigma\)- decompositions. The result presented here is the key procedure to a more general algorithm which is described fully in the author's Ph. D. thesis [Univ. Delaware (1983)].
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 12H99
zbMATH DE Number: 3940715
zbMATH Keywords: differential field
zbMATH Keywords: decision procedure for integrating a class of transcendental elementary functions
zbMATH Keywords: differential equation
MaRDI profile type: Publication
cites work: Q5820721
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description: scientific article; zbMATH DE number 3940715