The general analytic solution of a functional equation of addition type

H W Braden, V M Buchstaber

Research output: Contribution to journalArticlepeer-review

Abstract

The general analytic solution to the functional equation

GRAPHICS

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

phi(1)(x+y) = phi(4)(x)phi(5)(y) + phi(4)(y)phi(5)(x)

and

Psi(1)(x+y) = Psi(2)(x+y)phi(2)(x)phi(3)(y) + Psi(3)(x+y)phi(4)(x)phi(5)(y).

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

Keywords

  • functional equation
  • Calogero-Moser
  • special functions
  • MANY-BODY PROBLEMS
  • SYSTEMS
  • IDENTITIES

Cite this