Abstract
In this paper we derive a q-analog of Holman′s U( n) generalization of the Pfaff-Saalschutz or balanced 3 F 2 summation theorem. This provides a multivariable generalization of Jackson′s classical q-analog of the balanced 3 F 2 summation theorem. We obtain our main result from our new general q-difference equations for "balanced" basic hypergeometric series in U( n) and "both" q-analog of Holman′s U( n) generalization of the Vandermonde summation theorem. Even the classical case of our proof appears to be new. The q-analog of U( n) Pfaff-Saalschutz is invariant under inversion of the base q and also multivariable reversal of series. Corresponding theorems for ordinary series are deduced by taking the limit as q → 1 of all these results.
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