Abstract
Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered.
Original language | English |
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Pages (from-to) | 291-327 |
Number of pages | 37 |
Journal | Rocky Mountain Journal of Mathematics |
Volume | 43 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Generalized hypergeometric function
- Euler transformation
- Kummer transformation
- Quadratic transformations
- Summation theorem
- Zeros of entire functions