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A q-analog of the Gauss summation theorem for hypergeometric series in U(n). (English) Zbl 0658.33005
A q-analog of Holman’s U(n) generalization of the Gauss summation theorem for hypergeometric series is derived. This result is obtained by iterating the author’s generalization of the Gauss reduction formula for basic hypergeometric series in U(n). Multiple series generalizations of both q-analogs of the Chu-Vandermonde summation theorem occur as special cases. Letting $q\to 1$ the corresponding results for ordinary hypergeometric series in U(n) are obtained. U(n) generalizations the beta integral and Euler’s integral representation of a ${}_{2}{F}_{1}$ hypergeometric series are also given. Finally, some q-analogs of partial fractions expansions are discussed.
Reviewer: R.A.Gustafson

##### MSC:
 33C80 Connections of hypergeometric functions with groups and algebras 33C05 Classical hypergeometric functions, ${}_{2}{F}_{1}$ 33B15 Gamma, beta and polygamma functions