Theta hypergeometric series

By V. Spiridonov. 2003

74 citations recorded by the source corpus.

We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/14eb55a3932f856fb2bfa81d8a100b8443ceae4f

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Essays on the theory of elliptic hypergeometric functions (2008, background): “According to the general definition [10], formal series ∑”
$BC_n$-symmetric abelian functions (2004, background): “One immediate consequence is Spiridonov’s observation [25] that the various more traditionally hypergeometric special cases discussed following Theorem 4.”
Extensions of the well-poised and elliptic well-poised Bailey lemma (2003, unknown): “The rationale behind the above labelling of the r+1Vr series is that [ 18 ] (aq2k;p) (a;p) = (a1/2q, a1/2q,(a/p)1/2q, (ap)1/2q;q,p)k (a1/2, a1/2,(ap)1/2, (a/p)1/2;q,p)k ( q) k.”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Namely, we argue that for the existence of a non-trivial identity for an elliptic hypergeometric integral it is necessary to have a so-called totally elliptic hypergeometric term [82, 86, 90].”