# Elliptic Hypergeometric Functions

• Fokko J. van de Bult
Chapter
Part of the CRM Series in Mathematical Physics book series (CRM)

## Abstract

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.

## Notes

### Acknowledgements

I would like to express my gratitude to the organizers of ASIDE 2016 for inviting me to speak there. I would also like to thank an anonymous referee for his many useful remarks.

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