International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1995 / Article

Open Access

Volume 8 |Article ID 235869 | 6 pages | https://doi.org/10.1155/S1048953395000177

Transformation formulas for terminating Saalschützian hypergeometric series of unit argument

Received01 Jul 1994
Revised01 Nov 1994

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.

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.

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