A Generalization of Kummer's Identity

@article{Vidunas2000AGO,
  title={A Generalization of Kummer's Identity},
  author={Raimundas Vidunas},
  journal={Rocky Mountain Journal of Mathematics},
  year={2000},
  volume={32},
  pages={919-936}
}
  • R. Vidunas
  • Published 10 May 2000
  • Mathematics
  • Rocky Mountain Journal of Mathematics
The well-known formula of Kummer evaluates the hypergeometric series 2 F 1 () - 1) when the relation C - A + B = 1 holds. This paper deals with the evaluation of 2 F 1 (-1) series in the case when C - A + B is an integer. Such a series is expressed as a sum of two Γ-terms multiplied by terminating 3 F 2 (1) series. A few such formulas were essentially known to Whipple in the 1920s. Here we give a simpler and more complete overview of this type of evaluation. Additionally, algorithmic aspects of… 
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