Elliptic Hypergeometric Solutions to Elliptic Difference Equations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Author: Magnus, A.P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149168
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Elliptic Hypergeometric Solutions to Elliptic Difference Equations / A.P. Magnus // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 36 назв. — англ.

It is shown how to define difference equations on particular lattices {xn}, n ∊ 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 di...