Derivation of a $BC_n$ elliptic summation formula via the fundamental invariants

TL;DR

This paper presents an alternative proof of a $BC_n$ elliptic summation formula using fundamental invariants and Jackson integrals, contributing a new approach to elliptic hypergeometric identities.

Contribution

It introduces a novel proof method for the $BC_n$ elliptic summation formula leveraging fundamental $BC_n$ invariants and Jackson integrals.

Findings

New proof of the $BC_n$ elliptic summation formula

Application of fundamental $BC_n$ invariants to elliptic hypergeometric sums

Enhanced understanding of Jackson integrals in elliptic summations

Abstract

We give an alternative proof of an elliptic summation formula of type $BC_n$ by applying the fundamental $BC_n$ invariants to the study of Jackson integrals associated with the summation formula.