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Abstract
We study multiple series extensions of basic hypergeometric series related to the root system Dn. We make a small change in the notation used for Cn and Dn series to bring them closer to An series. This allows us to combine the three types of series, and get Dn extensions of the following classical summation and transformation theorems: The q-Pfaff-Saalschutz summation, Rogers' 6 φ5 sum, the q-Gauss summation, q-Chu-Vandermonde summations, Watson's q-analogue of Whipple's transformation, and the q-Dougall summation theorem. We also define An and Cn extensions of the Rogers-Selberg function, and prove a reduction formula for both of them. This generalizes some work of Andrews. We use some techniques originally developed to study multiple basic hypergeometric series related to the root system An (U(n + 1) basic hypergeometric series).
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