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On a claim of Ramanujan about certain hypergeometric series


Author: David Bradley
Journal: Proc. Amer. Math. Soc. 121 (1994), 1145-1149
MSC: Primary 33C20
DOI: https://doi.org/10.1090/S0002-9939-1994-1189537-5
MathSciNet review: 1189537
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Abstract: We state and prove a claim of Ramanujan. As a consequence, a large new class of Saalschützian hypergeometric series is summed in closed form.


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

  • [1] Richard Askey and Mourad Ismail, A combinatorial sum, MRC Technical Summary Report #1557, July 1975, unpublished.
  • [2] W. N. Bailey, Generalized hypergeometric series, Cambridge Univ. Press, London, 1935.
  • [3] Bruce C. Berndt, Ramanujan’s notebooks. Part II, Springer-Verlag, New York, 1989. MR 970033
  • [4] G. H. Hardy, A chapter from Ramanujan's note-book, Proc. Cambridge Philos. Soc. 21 (1923), 492-503.
  • [5] Srinivasa Ramanujan, Notebooks. Vols. 1, 2, Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904

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DOI: https://doi.org/10.1090/S0002-9939-1994-1189537-5
Article copyright: © Copyright 1994 American Mathematical Society