Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x)
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.
- Publication:
-
Zeitschrift Angewandte Mathematik und Physik
- Pub Date:
- February 2011
- DOI:
- Bibcode:
- 2011ZaMP...62...31M
- Keywords:
-
- 33C15;
- 33C20;
- 33C50;
- Generalized hypergeometric function;
- Euler transformation;
- Kummer transformation