\(D_n\) basic hypergeometric series (Q1306583)

The purpose of this paper is the study of multiple series extensions of basic hypergeometric series related to the root system \(D_n\). The starting point in this paper is a small change in the notation of \(C_n\) and \(D_n\) series to bring them closer to \(A_n\) series. In this manner three types of series are combined and \(D_n\) extensions of a string of summation and transformation formulas are derived. \(A_n\)- and \(C_n\)-extensions of the Rogers-Selberg function are also defined and a reduction formula is proved for both of them which generalizes some work of Andrews.