Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Abstract

It is shown how to define difference equations on particular lattices {x_n}, n in 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.

Keywords

• elliptic difference equations
• elliptic hypergeometric expansions