Classical elliptic hypergeometric functions and their applications

Abstract

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric function and some of its properties are described. Present review is based on author's habilitation thesis [Spi7] containing a more detailed account of the subject.

42 pages, typos removed, references updated

References in corpus (2)

• Unit circle elliptic beta integrals
• Transformations of elliptic hypergometric integrals

Cited by in corpus (5)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• A duality web of linear quivers
• Limits of elliptic hypergeometric integrals
• A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring