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Mathematics > Classical Analysis and ODEs

arXiv:0712.4253 (math)
[Submitted on 27 Dec 2007 (v1), last revised 20 Mar 2009 (this version, v2)]

Title:Determinants of elliptic hypergeometric integrals

Authors:E.M. Rains, V.P. Spiridonov
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Abstract: We start from an interpretation of the $BC_2$-symmetric "Type I" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, by proving both sides satisfy the same difference equations, and that the difference equations satisfy a Galois-theoretical condition that ensures uniqueness of simultaneous solution.
Comments: 17 pages; minor modifications
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 11C20, 33E99
Cite as: arXiv:0712.4253 [math.CA]
  (or arXiv:0712.4253v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.0712.4253
Journal reference: Funct. Analysis and its Appl. 43 (2009), no. 4, 297-311

Submission history

From: Vyacheslav P. Spiridonov [view email]
[v1] Thu, 27 Dec 2007 19:37:41 UTC (17 KB)
[v2] Fri, 20 Mar 2009 14:36:35 UTC (17 KB)
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