Essays on the theory of elliptic hypergeometric functions

By V. Spiridonov. 2008

164 citations recorded by the source corpus.

This is a brief survey of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. A proof is given of the most general known univariate exact integration formula generalizing Euler's beta integral. It is called the elliptic beta integral. An elliptic analogue of the Gauss hypergeometric function is constructed together with the elliptic hypergeometric equation for it. Biorthogonality relations for this function and its particular subcases are described. The known elliptic beta integrals on root systems are listed, and symmetry transformations are considered for the corresponding higher-order elliptic hypergeometric functions.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/44e51fd3aa31fbbc68f59b096ea0966d0d3e4791

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

1. G. Vartanov
2. Christian Krattenthaler
3. Shlomo S. Razamat
4. L. Rastelli
5. Abhijit Gadde
6. Wenbin Yan
7. D. Gaiotto
8. V. Spiridonov

In Applied Mathematics

1. G. Vartanov
2. Christian Krattenthaler
3. Abhijit Gadde
4. Shlomo S. Razamat
5. L. Rastelli
6. Wenbin Yan
7. D. Gaiotto
8. V. Spiridonov

In Computational Theory and Mathematics

1. G. Vartanov
2. Christian Krattenthaler
3. Shlomo S. Razamat
4. L. Rastelli
5. Abhijit Gadde
6. Wenbin Yan
7. V. Spiridonov
8. D. Gaiotto

Citations in the corpus

• Bootstrapping the superconformal index with surface defects (2012, background): “See also [46] for a nice review of the properties of elliptic Gamma functions.”
• The superconformal index of the E6 SCFT (2010, background): “8) For reviews of the elliptic Gamma function and of elliptic hypergeometric mathematics the reader can consult [17, 18, 19].”
• Elliptic Hypergeometry of Supersymmetric Dualities (2009, methodology): “Vershik for persistent support and encouragement, which was the main driving force for writing the survey [89].”
• Superconformal indices of three-dimensional theories related by mirror symmetry (2011, methodology): “All four forms correspond to the W (E6) Weyl group symmetry of the elliptic beta integral evaluation formula [4, 5].”