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arXiv · 0903.4803

Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Alphonse P. Magnus
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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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Alphonse P. Magnus. 2009-03-27. Elliptic Hypergeometric Solutions to Elliptic Difference Equations. https://doi.org/10.3842/sigma.2009.038

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