A functional equation and Jacobian elliptic functions
type: Item
instance of: scholarly article
title: A functional equation and Jacobian elliptic functions
zbMATH Open document ID: 0911.39013
author: Shaun Cooper
published in: Aequationes Mathematicae
publication date: 1999-04-28T00:00:00Z
review text: This paper is concerned with the functional equation \(\frac{f(x+y)}{f(x-y)}=\frac{g(x)+g(y)}{g(x)-g(y)}\) where \(f\) and \(g\) are meromorphic functions. It is shown that the general solution can be given in terms of Jacobian elliptic functions, or trigonometric or linear functions obtained thereof as limiting cases. Special consideration is given to solutions which are real on the real axis.
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 1220998
zbMATH Keywords: meromorphic functions
zbMATH Keywords: general solution
zbMATH Keywords: Jacobian elliptic functions
zbMATH Keywords: trigonometric or linear functions
reviewed by: Walter Bergweiler
MaRDI profile type: Publication
full work available at URL: s000100050045
OpenAlex ID: W2059559374
DOI: 10.1007/S000100050045
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description: scientific article; zbMATH DE number 1220998