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Elliptic Hypergeometric Solutions to Elliptic Difference Equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Elliptic Hypergeometric Solutions to Elliptic Difference Equations
Інший ID:
2000 Mathematics Subject Classification: 39A70; 41A20
Посилання:
Elliptic Hypergeometric Solutions to Elliptic Difference Equations / A.P. Magnus // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 36 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). Many thanks to the organizers of the workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (Hausdorf f Center for Mathematics, Bonn, July 2008), to A. Aptekarev, B. Beckermann, A.C. Matos, F. Wielonsky, of the Laboratoire Paul Painlev´e UMR 8524, Universit´e de Lille 1, France, who organized their 3`emes Journ´ees Approximation on May 15–16, 2008. Many thanks too to R. Askey, L. Haine, M. Ismail, F. Nijhof f, A. Ronveaux, and, of course, V. Spiridonov and A. Zhedanov for their preprints, interest, remarks, and kind words. Many thanks to the referees for expert and careful reading, and kind words too. This paper presents research results of the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office.
Дата:
2009
Переглядів:
362
Завантажень:
205
Анотація:
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 difference equations of first order are considered here.
