Transformation formulas for terminating Saalschützian hypergeometric series of unit argument. (1995) - Bühring, Wolfgang
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.