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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 q1 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

33C80Connections of hypergeometric functions with groups and algebras
33C05Classical hypergeometric functions, 2 F 1
33B15Gamma, beta and polygamma functions