Corollaries and multiple extensions of Gessel and Stanton hypergeometric summation formulas

  • Thomas Ernst Uppsala University
  • Per W. Karlsson Uppsala University
Keywords: simple and multiple hypergeometric formulas, reversion, Pfaff-Kummer and Euler transformations

Abstract

We find some new simple hypergeometric formulas in the footsteps of the important article by Gessel and Stanton. These are multiple reduction formulas, multiple summation formulas, as well as multiple transformation formulas for special Kampé de Fériet functions and Appell functions. The hypergeometric summation formulas have special function arguments in Q and parameter values in N or C. The proofs use Pfaff-Kummer transformation, Euler transformation, or an improved form of Slater reversion.

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Published
2021-06-21
Section
Articles