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SIGMA, 2009, Volume 5, 038, 12 pages (Mi sigma384)  

This article is cited in 2 scientific papers (total in 2 papers)

Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Alphonse P. Magnus

Université catholique de Louvain, Institut mathématique, 2 Chemin du Cyclotron, B-1348 Louvain-La-Neuve, Belgium

Abstract: 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.

Keywords: elliptic difference equations; elliptic hypergeometric expansions

DOI: https://doi.org/10.3842/SIGMA.2009.038

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Full text: http://emis.mi.ras.ru/.../038
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Bibliographic databases:

ArXiv: 0903.4803
MSC: 39A70; 41A20
Received: December 1, 2008; in final form March 20, 2009; Published online March 27, 2009
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Citation: Alphonse P. Magnus, “Elliptic Hypergeometric Solutions to Elliptic Difference Equations”, SIGMA, 5 (2009), 038, 12 pp.

Citation in format AMSBIB
\Bibitem{Mag09}
\by Alphonse P.~Magnus
\paper Elliptic Hypergeometric Solutions to Elliptic Difference Equations
\jour SIGMA
\yr 2009
\vol 5
\papernumber 038
\totalpages 12
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Witte N.S., “Semiclassical Orthogonal Polynomial Systems on Nonuniform Lattices, Deformations of the Askey Table, and Analogues of Isomonodromy”, Nagoya Math. J., 219 (2015), 127–234  crossref  mathscinet  zmath  isi  elib  scopus
    2. Chiang Y.-M., Feng Sh., “Nevanlinna Theory of the Askey–Wilson Divided Difference Operator”, Adv. Math., 329 (2018), 217–272  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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