Transformation formulas for terminating Saalschützian hypergeometric series of unit argument
Transformation formulas for terminating Saalschützian hypergeometric series of unit argument are presented. They generalize the Saalschützian summation formula for . Formulas for are obtained explicitly, and a recurrence relation is proved by means of which the corresponding formulas can also be derived for larger . 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 series are found. They depend on four or six independent parameters, respectively.
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