# Gustafson-Rakha-Type Elliptic Hypergeometric Series

## TL;DR

This paper proves a new multivariable elliptic extension of Jackson's summation formula, generalizing previous results and introducing novel elliptic summations and Bailey transformations with broad mathematical implications.

## Contribution

It provides the first multivariable elliptic extension of Jackson's summation conjecture, including new elliptic identities and transformations.

## Key findings

- Proved a multivariable elliptic Jackson summation formula.
- Derived two new multivariable elliptic Jackson summations.
- Established two novel multivariable elliptic Bailey transformations.

## Abstract

We prove a multivariable elliptic extension of Jackson's summation formula conjectured by Spiridonov. The trigonometric limit case of this result is due to Gustafson and Rakha. As applications, we obtain two further multivariable elliptic Jackson summations and two multivariable elliptic Bailey transformations. The latter four results are all new even in the trigonometric case.