Extensions of the Classical Transformations of the Hypergeometric Function 3F2

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It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function 3F2 can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple’s identity relating very well poised 7F6(1) series and balanced 4F3(1) series, and extensions of other summation identities.

MSC Codes Primary 33C20, 33C45

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Aug 9 2018


  • Discrete orthogonal polynomial
  • Generalized hypergeometric function
  • Hypergeometric transformation
  • Summation identity

ASJC Scopus subject areas

  • General

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