A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $BC_n$

TL;DR

This paper extends the Sears--Slater transformation to elliptic Lagrange interpolation functions for type BC_n Jackson integrals, providing explicit formulas and solutions for related q-difference systems.

Contribution

It introduces a generalized transformation and explicit determinant formulas for elliptic Lagrange interpolation functions in the context of type BC_n Jackson integrals.

Findings

Derived a connection formula as a linear combination of bilateral series.

Expressed coefficients using elliptic Lagrange interpolation functions.

Provided an explicit determinant formula for the fundamental solution matrix.

Abstract

The connection formula for the Jackson integral of type $BC_n$ is obtained in the form of a Sears--Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple series. The coefficients of this expansion are expressed by certain elliptic Lagrange interpolation functions. Analyzing basic properties of the elliptic Lagrange interpolation functions, an explicit determinant formula is provided for a fundamental solution matrix of the associated system of $q$-difference equations.