Euler-type transformations for the generalized hypergeometric function r+2 F r+1(x)

  • A. R. MillerEmail author
  • R. B. Paris


We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for r+1 F r+1 (x) that was recently derived in a different way.

Mathematics Subject Classification (2000)

33C15 33C20 33C50 


Generalized hypergeometric function Euler transformation Kummer transformation 


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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.WashingtonUSA
  2. 2.Division of Complex SystemsUniversity of Abertay DundeeDundeeUK

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