Short proofs of the elliptic beta integrals
By V. Spiridonov. 2004
50 citations recorded by the source corpus.
We give elementary proofs of the univariate elliptic beta integral with bases |q|,|p| < 1 and its multiparameter generalizations to integrals on the An and Cn root systems. We prove also some new unit circle multiple elliptic beta integrals, which are well defined for |q| = 1, and their p → 0 degenerations.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/28e6d6828edb9d83c0906d03b46738ab8995a662
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- G. Vartanov
- V. Spiridonov
- S. Ole Warnaar
- A. Selberg
- Peter J. Forrester
- Eric M. Rains
- Hjalmar Rosengren
- Jeremy Lovejoy
In Applied Mathematics
- G. Vartanov
- V. Spiridonov
- S. Ole Warnaar
- A. Selberg
- Peter J. Forrester
- Eric M. Rains
- Hjalmar Rosengren
- Christian Krattenthaler
Citations in the corpus
- Essays on the theory of elliptic hypergeometric functions (2008, methodology): “Here we presented the proof obtained in the paper [43], which generalizes the method of computation of the Askey–Wilson integral from [44].”
- Inversions of integral operators and elliptic beta integrals on root systems (2004, methodology): “More elementary proofs using difference equations were subsequently given in [26].”
- Elliptic Hypergeometry of Supersymmetric Dualities (2009, methodology): “Two totally elliptic hypergeometric terms associated with the elliptic beta integrals of type I on root systems BCn [20] and An [83] were constructed in [86].”
- The importance of the Selberg integral (2007, methodology): “J.F. van Diejen and Spiridonov [36] have given an n-dimensional generalization of (3.72) which may be viewed as an elliptic extension of the Selberg integral.”