Elliptic Hypergeometric Solutions to Elliptic Difference Equations
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149168 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656946255953920 |
|---|---|
| author | Magnus, A.P. |
| author_facet | Magnus, A.P. |
| citation_txt | Elliptic Hypergeometric Solutions to Elliptic Difference Equations / A.P. Magnus // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 36 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-02T05:41:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149168 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T05:41:34Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Magnus, A.P. 2019-02-19T17:55:43Z 2019-02-19T17:55:43Z 2009 Elliptic Hypergeometric Solutions to Elliptic Difference Equations / A.P. Magnus // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 36 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 39A70; 41A20 https://nasplib.isofts.kiev.ua/handle/123456789/149168 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Elliptic Hypergeometric Solutions to Elliptic Difference Equations Article published earlier |
| spellingShingle | Elliptic Hypergeometric Solutions to Elliptic Difference Equations Magnus, A.P. |
| title | Elliptic Hypergeometric Solutions to Elliptic Difference Equations |
| title_full | Elliptic Hypergeometric Solutions to Elliptic Difference Equations |
| title_fullStr | Elliptic Hypergeometric Solutions to Elliptic Difference Equations |
| title_full_unstemmed | Elliptic Hypergeometric Solutions to Elliptic Difference Equations |
| title_short | Elliptic Hypergeometric Solutions to Elliptic Difference Equations |
| title_sort | elliptic hypergeometric solutions to elliptic difference equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149168 |
| work_keys_str_mv | AT magnusap elliptichypergeometricsolutionstoellipticdifferenceequations |