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Some summation formulas for the series $ \sb 3F\sb 2(1)$


Author: J.-L. Lavoie
Journal: Math. Comp. 49 (1987), 269-274
MSC: Primary 33A30; Secondary 33A15
DOI: https://doi.org/10.1090/S0025-5718-1987-0890268-1
MathSciNet review: 890268
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Abstract | References | Similar Articles | Additional Information

Abstract: Summation formulas, contiguous to Watson's and Whipple's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.


References [Enhancements On Off] (What's this?)

  • [1] W. N. Bailey, Generalized Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1935.
  • [2] G. H. Hardy, "A chapter from Ramanujan's note-book," Proc. Cambridge Philos. Soc., v. 21, 1923, pp. 492-503.
  • [3] E. E. Kummer, "Über die hypergeometrische Reihe $ F(a;b;x)$," J. Reine Angew. Math., v. 15, 1836, pp. 127-172.
  • [4] J. L. Lavoie, "Some evaluations for the generalized hypergeometric series," Math. Comp., v. 46, 1986, pp. 215-218. MR 815842 (87c:33007)
  • [5] E. D. Rainville, Special Functions, Macmillan, New York, 1960. MR 0107725 (21:6447)
  • [6] G. N. Watson, "The integral formula for generalized Legendre functions," Proc. London Math. Soc. (2), v. 17, 1917, pp. 241-246.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0890268-1
Keywords: Generalized hypergeometric functions of one variable, gamma function, psi function
Article copyright: © Copyright 1987 American Mathematical Society

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