A generalization of the Sears-Slater transformation and elliptic Lagrange interpolation of type \(BC_{n}\) (Q2629109)

The authors obtain a connection formula for the Jackson integral of type \(BC_n\) (introduced by \textit{K. Aomoto} and \textit{M. Ito} in the same journal [ibid. 221, No. 4, 1069--1114 (2009; Zbl 1173.33013)]) in the form of a Sears-Slater type expansion of a bilateral multiple hypergeometric series as a linear combination of certain specific bilateral multiple series. They give also the coefficients of this expansion in terms of certain elliptic Lagrange interpolation functions. An explicit determinant formula for a fundamental solutions matrix of a system of \(q\)-difference equations is also provided.