# A determinant formula associated with the elliptic hypergeometric integrals of type $BC_n$

## TL;DR

This paper derives a determinant formula for elliptic hypergeometric integrals of type BC_n by analyzing q-difference equations and asymptotic behavior, advancing the understanding of their algebraic structure.

## Contribution

It introduces a new determinant formula for elliptic hypergeometric integrals of type BC_n using q-difference equations and asymptotic analysis.

## Key findings

- Established a determinant formula for the bilinear form of elliptic hypergeometric integrals of type BC_n
- Connected elliptic interpolation functions to the study of q-difference equations
- Provided asymptotic analysis along singularities to prove the formula

## Abstract

We establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type $BC_n$ by studying the structure of $q$-difference equations to be satisfied by them. The determinant formula is proved by combining the $q$-difference equations of the determinant and its asymptotic analysis along the singularities. The elliptic interpolation functions of type $BC_n$ are essentially used in the study of the $q$-difference equations.