  We investigate the connection problem for the Jackson integral of type $A_n$.
Our connection formula implies a Slater type expansion of a bilateral multiple
basic hypergeometric series as a linear combination of several specific
multiple series. Introducing certain elliptic Lagrange interpolation functions,
we determine the explicit form of the connection coefficients. We also use
basic properties of the interpolation functions to establish an explicit
determinant formula for a fundamental solution matrix of the associated system
of $q$-difference equations.
