Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Details Elliptic Hypergeometric Solutions to Elliptic Difference Equations Elliptic Hypergeometric Solutions to Elliptic Difference Equations

2009-03-27

arxiv.org/abs/0903.4803v1

SIGMA 5 (2009), 038, 12 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2009.038

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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