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+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.
| Original language | English |
|---|---|
| Pages (from-to) | 31–45 |
| Number of pages | 15 |
| Journal | Zeitschrift fur Angewandte Mathematik und Physik |
| Volume | 62 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Feb 2011 |
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Miller, A. R., & Paris, R. B. (2011). Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x). Zeitschrift fur Angewandte Mathematik und Physik, 62(1), 31–45. https://doi.org/10.1007/s00033-010-0085-0