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A NOTE ON GAUSS'S SECOND SUMMATION THEOREM FOR THE SERIES 2F1(1/2)

Choi, June-Sang;Rathie, Arjun K.;Purnima, Purnima

  • Published : 2007.10.31

Abstract

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

Keywords

generalized hypergeometric series $_pF_q$;Gauss's second summation theorem for $_2F_1(1/2)$;Beta function

References

  1. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
  2. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935

Cited by

  1. NOTE ON THE CLASSICAL WATSON'S THEOREM FOR THE SERIES3F2 vol.35, pp.4, 2013, https://doi.org/10.5831/HMJ.2013.35.4.701
  2. A generalization of a formula due to Kummer† vol.22, pp.11, 2011, https://doi.org/10.1080/10652469.2011.588786
  3. Generalizations of classical summation theorems for the series2F1and3F2with applications vol.22, pp.11, 2011, https://doi.org/10.1080/10652469.2010.549487