Permutation symmetry for theta functions
type: Item
instance of: scholarly article
title: Permutation symmetry for theta functions
zbMATH Open document ID: 1220.33019
author: B. C. Carlson
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-03-14T00:00:00Z
review text: This article does for combinations of theta functions most of what the author [\textit{B.C. Carlson}, ``Symmetry in \(c\), \(d\), \(n\) of Jacobian elliptic functions,'' J. Math. Anal. Appl. 299, No.\,1, 242--253 (2004; Zbl 1061.33019)] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral \(R_F\) of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters \(c, d, n\) for the Jacobian case but now in the subscript \(2, 3, 4\) for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas. The formulas in Section 2.2. are known; the other formulas are concise expressions for old and new theta function formulas. A most interesting paper.
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 5865634
zbMATH Keywords: theta functions
zbMATH Keywords: phi functions
zbMATH Keywords: permutation symmetry
zbMATH Keywords: symmetric elliptic integral
zbMATH Keywords: Jacobian elliptic functions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.01.030
OpenAlex ID: W2082836056
cites work: Symmetry in c, d, n of Jacobian elliptic functions
cites work: Q3675135
cites work: Q3844537
cites work: Q3278470
cites work: Generating Functions for Bessel and Related Polynomials
DOI: 10.1016/J.JMAA.2011.01.030
description: scientific article; zbMATH DE number 5865634