On the elliptic beta function

By V. Spiridonov. 2001

189 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f2b1abb03ddb0d32f3421053c00700774dd7b1db

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Transformations of elliptic hypergeometric integrals (2010, background): “A direct proof of the corollary has since been given by Spiridonov [33]; see also the remark following the second proof of Theorem 6.1 below.”
Reducing the 4d index to the S3 partition function (2011, background): “1) where Γ is the elliptic gamma function [20] defined to be Γ(z; r, s) = ∏”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “The elliptic beta integral As a first example of elliptic hypergeometric functions we describe the elliptic beta integral, which was discovered by the author in [29].”
Inversions of integral operators and elliptic beta integrals on root systems (2004, background): “Elliptic beta integrals The single-variable elliptic beta integral — due to the first author [22] — corresponds to the following generalization of the celebrated Rahman integral [16] (obtained as an important special case of the Nassrallah–Rahman integral [15]).”
Supersymmetry on curved spaces and holography (2012, background): “In fact, it involves recently discovered identities on elliptic hypergeometric integrals [26, 27].”
Transformations of elliptic hypergometric integrals (2003, background): “For m = 0, we obtain the following integral conjectured by Spiridonov [32]: Corollary 4.2.”
Superconformal indices of three-dimensional theories related by mirror symmetry (2011, methodology): “In this case, the indices are described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn [4].”
Applications of the superconformal index for protected operators and q-hypergeometric identities to N=1 dual theories (2008, methodology): “A generalisation of the Nassrallah-Rahman theorem by Spiridonov [14], involving elliptic gamma functions, is shown here to be directly equivalent to the required Nc = 2, Nf = 3 superconformal index identity.”
FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS (2011, background): “Technically, this fact is realized by the reduction of elliptic hypergeometric integrals [2] to hyperbolic q-hypergeometric integrals, which was rigorously established by Rains in [27].”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, methodology): “As to the proofs of many new hypergeometric identities conjectured in this paper, we refer to known methods described in [19, 20, 65, 69, 81, 83, 84, 93] (or indicated above in some cases) which are available for their treatment.”