The general analytic solution of a functional equation of addition type

H. W. Braden, V. M. Buchstaber

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

The general analytic solution to the functional equation (equation presented) is characterized. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations φ1 (x + y) = φ4(x)φ5(y) + φ4(y)φ5(x) and ψ1(x + y) = ψ2(x + y)φ2(x)φ3(y) + ψ3(x + y)φ4(x)φ5(y).

Original languageEnglish
Pages (from-to)903-923
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume28
Issue number4
DOIs
Publication statusPublished - Jul 1997
Externally publishedYes

Keywords

  • Calogero-Moser
  • Functional equation
  • Special functions

Fingerprint

Dive into the research topics of 'The general analytic solution of a functional equation of addition type'. Together they form a unique fingerprint.

Cite this