Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 2, Pages 189-194
doi: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 Wolfgang Bühring. 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.