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.

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Cited by in corpus (3)

• Elliptic hypergeometric functions
• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions