Three-term relations between interpolation polynomials for a [formula omitted]-type basic hypergeometric series

Abstract

We present an explicit expression for the q-difference system of rank n+1 satisfied by a BCn-type Jackson integral (q-series) as first order simultaneous q-difference equations with a concrete basis. For this purpose we introduce two types of symmetric Laurent polynomials called the interpolation polynomials. Three-term relations between the interpolation polynomials play an essential role in deriving the q-difference system. As an application, we give another proof for the product formula of the q-integral introduced by Gustafson.