Zeitschrift für angewandte Mathematik und Physik

, Volume 62, Issue 1, pp 31–45

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


DOI: 10.1007/s00033-010-0085-0

Cite this article as:
Miller, A.R. & Paris, R.B. Z. Angew. Math. Phys. (2011) 62: 31. doi:10.1007/s00033-010-0085-0


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 


Generalized hypergeometric function Euler transformation Kummer transformation 

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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