Permutation symmetry for theta functions

TitlePermutation symmetry for theta functions
Publication TypeJournal Article
Year of Publication2011
AuthorsCarlson BC
Journal TitleJournal of Mathematical Analysis and Applications
Date Published01
Type of ArticleArticle
ISBN Number0022-247X
Accession NumberISI:000287571500004
Keywordselliptic integral, Jacobian elliptic functions, Permutation symmetry, Phi functions, Symmetric, Theta functions

This paper does for combinations of theta functions most of what Carlson (2004) [1] 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 subscripts 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. Published by Elsevier Inc.

URL<Go to ISI>://000287571500004
Alternate JournalJ. Math. Anal. Appl.