Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Magnus, Alphonse
(2009) Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions — Location: Bonn(Germany) (21.July.2008)

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  • Magnus, AlphonseUCLouvain
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Abstract
It is shown how to define difference equations on particular lattices {x(n)}, n is an element of 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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Magnus, A. (2009). Elliptic Hypergeometric Solutions to Elliptic Difference Equations. Symmetry Integrability And Geometry-methods And Applications, 5. https://doi.org/10.3842/SIGMA.2009.038 (Original work published 2009)