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

Article

Abstract

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+2Fr+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+1Fr+1 (x) that was recently derived in a different way.

Mathematics Subject Classification (2000)

33C15 33C20 33C50 

Keywords

Generalized hypergeometric function Euler transformation Kummer transformation 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

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

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