Elliptic hypergeometric functions

Abstract

This is a brief overview of the status of the theory of elliptic hypergeometric functions to the end of 2012 written as a complementary chapter to the Russian edition of the book by G.E. Andrews, R. Askey, and R. Roy, Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999.

27 pp., a complement to the book by G.E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Math. Appl. 71, Cambridge Univ. Press, Cambridge, 1999, written for its Russian edition: Moscow, MCCME, 2013, pp. 577-606

References in corpus (7)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Properties of generalized univariate hypergeometric functions
• Elliptic enumeration of nonintersecting lattice paths
• Yang-Baxter R operators and parameter permutations
• An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
• Elliptic Littlewood identities
• Elliptic Hypergeometric Solutions to Elliptic Difference Equations

Cited by in corpus (12)

• The Geometry of Supersymmetric Partition Functions
• Essays on the theory of elliptic hypergeometric functions
• Exceptional Indices
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• The star-triangle relation and 3d superconformal indices
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Surface defects in E-string compactifications and the van Diejen model
• Complex hypergeometric functions and integrable many-body problems
• Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group
• Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
• Macdonald Polynomials and Multivariable Basic Hypergeometric Series
• Rahman's biorthogonal functions and superconformal indices