  Basic Harish-Chandra series are asymptotically free meromorphic solutions of
the system of basic hypergeometric difference equations associated to root
systems. The associated connection coefficients are explicitly computed in
terms of Jacobi theta functions. We interpret the connection coefficients as
the transition functions for asymptotically free meromorphic solutions of
Cherednik's root system analogs of the quantum Knizhnik-Zamolodchikov
equations. They thus give rise to explicit elliptic solutions of root system
analogs of dynamical Yang-Baxter and reflection equations. Applications to
quantum c-functions, basic hypergeometric functions, reflectionless difference
operators and multivariable Baker-Akhiezer functions are discussed.
