Bounds for symmetric elliptic integrals.
type: Item
instance of: scholarly article
title: Bounds for symmetric elliptic integrals.
zbMATH Open document ID: 1041.33015
DOI: 10.1016/S0021-9045(03)00077-7
author: Edward Neuman
published in: Journal of Approximation Theory
publication date: 2003-07-01T00:00:00Z
review text: In this paper the author derives lower and upper bounds for the four standard incomplete symmetric elliptic integrals. The bounding functions are expressed in terms of the elementary transcendental functions. All elliptic integrals delt with in this paper can be represented by the \(R\)-hypergeometric functions introduced in [\textit{B. C. Carlson}, Special Functions of Applied Mathematics, Academic Press, New York (1977; Zbl 0394.33001)]. Sharp bounds for the ratio of the complete elliptic integrals of the first and second kind are also obtained. These results can be used to obtain bounds for the product of these integrals. It is shown that an iterative numerical algorithm for computing the ratios and products of complete integrals has the second order of convergence.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 1944991
zbMATH Keywords: standard elliptic integrals
zbMATH Keywords: The \(R\)-hypergeometric functions
zbMATH Keywords: Inequalities
zbMATH Keywords: Means
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1944991