Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 038, 12 pages      arXiv:0903.4803
Contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions”

Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Alphonse P. Magnus
Université catholique de Louvain, Institut mathématique, 2 Chemin du Cyclotron, B-1348 Louvain-La-Neuve, Belgium

Received December 01, 2008, in final form March 20, 2009; Published online March 27, 2009

It is shown how to define difference equations on particular lattices {xn}, n Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

Key words: elliptic difference equations; elliptic hypergeometric expansions.

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