Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Abstract

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

References in corpus (3)

• Essays on the theory of elliptic hypergeometric functions
• Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
• A Critical Phenomenon in Solitonic Ising Chains