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Journal of Applied Mathematics and Stochastic Analysis
Volume 8, Issue 2, Pages 189-194
http://dx.doi.org/10.1155/S1048953395000177

Transformation formulas for terminating Saalschützian hypergeometric series of unit argument

Universität Heidelberg, Physikalisches Institut, Heidelberg D-69120, Germany

Received 1 July 1994; Revised 1 November 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Transformation formulas for terminating Saalschützian hypergeometric series of unit argument p+1Fp(1) are presented. They generalize the Saalschützian summation formula for 3F2(1). Formulas for p=3,4,5 are obtained explicitly, and a recurrence relation is proved by means of which the corresponding formulas can also be derived for larger p. The Gaussian summation formula can be derived from the Saalschützian formula by a limiting process, and the same is true for the corresponding generalized formulas. By comparison with generalized Gaussian summation formulas obtained earlier in a different way, two identities for finite sums involving terminating 3F2(1) series are found. They depend on four or six independent parameters, respectively.