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Note on the Bradley and Ramanujan summation


Author: Chu Wenchang
Journal: Proc. Amer. Math. Soc. 124 (1996), 3753-3754
MSC (1991): Primary 33A30; Secondary 05A19
DOI: https://doi.org/10.1090/S0002-9939-96-03525-3
MathSciNet review: 1343730
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Abstract: The hypergeometric series of Bradley and Ramanujan is evaluated by means of the binomial convolutions of Hagen and Rothe, which presents, alternatively, a short proof of the recent result of Bradley about Ramanujan's enigmatic claim.


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

  • 1. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.
  • 2. D. Bradley, On a claim of Ramanujan about certian hypergeometric series, Proc. Amer. Math. Soc.121:4 (1994), 1145-1149. MR 94j:33003
  • 3. W. Ch. Chu, Inversion techniques and combinatorial identities, Boll. UMI(7) 7-B (1993), 737-760. MR 95e:33006
  • 4. W. Ch. Chu & L. C. Hsu, Some new applications of Gould-Hsu inversions, J. Combin. Informat. & System Science 14:1 (1990), 1-4. MR 92c:05018
  • 5. H. W. Gould, Some generalizations of Vandermonde's convolution, Amer. Math. Month.63:1 (1956), 84-91. MR 17:702g

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Additional Information

Chu Wenchang
Affiliation: Istituto di Matematica, “Guido Castelnuovo”, Universit\a‘a degli Studi di Roma “La Sapienza”, Roma, Italia
Email: WENCHANG@mat.uniroma1.it

DOI: https://doi.org/10.1090/S0002-9939-96-03525-3
Keywords: Binomial convolution, Hypergeometric series, The Gauss summation theorem
Received by editor(s): January 3, 1995
Received by editor(s) in revised form: May 23, 1995
Additional Notes: The author was partially supported by IAMI (CNR, Milano), 1994
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

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