Transformation formulas for terminating Saalschützian hypergeometric series of unit argument. (1995)

• Record Type: Journal Article
• Authors: Bühring, Wolfgang
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 8:Number 2(1995)
• Page Start: 189
• Page End: 194
• Publication Date: 1995
• Subjects: hypergeometric series -- summation formula of Saalschütz -- Gaussian summation formula; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953395000177
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Transformation formulas for terminating Saalschützian hypergeometric series of unit argument p + 1 F p ( 1 ) are presented. They generalize the Saalschützian summation formula for 3 F 2 ( 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 3 F 2 ( 1 ) series are found. They depend on four or six independent parameters, respectively.