Elliptic Hypergeometric Functions

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


These lecture notes discuss some of the basics of elliptic hypergeometric functions. These are fairly recent generalizations of ordinary hypergeometric functions. In this chapter we first discuss both ordinary hypergeometric functions and elliptic functions, as you need to know both to define elliptic hypergeometric series. We subsequently discuss some of the important properties these series satisfy, in particular we consider the biorthogonal functions found by Spiridonov and Zhedanov, both with respect to discrete and continuous measure. In doing so we naturally encounter the most important evaluation and transformation formulas for elliptic hypergeometric series, and for the associated elliptic beta integral.
Original languageEnglish
Title of host publicationSymmetries and Integrability of Difference Equations
Subtitle of host publicationLecture Notes of the Abecederian School of SIDE 12, Montreal 2016
EditorsDecio Levi, Raphaël Rebelo, Pavel Winternitz
Place of PublicationCham
Number of pages32
ISBN (Electronic)978-3-319-85967-5
ISBN (Print)978-3-319-56665-8
Publication statusPublished - 2017

Publication series

NameCRM Series in Mathematical Physics


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