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Transformation formulas for terminating Saalschützian hypergeometric series of unit argument

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  • Wolfgang Bühring

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.

Suggested Citation

  • Wolfgang Bühring, 1995. "Transformation formulas for terminating Saalschützian hypergeometric series of unit argument," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-6, January.
    • Handle: RePEc:hin:jnijsa:235869
    DOI: 10.1155/S1048953395000177
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