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Note on the Bradley and Ramanujan summation
Author(s):
Chu
Wenchang
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3753-3754.
MSC (1991):
Primary 33A30;
Secondary 05A19
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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:
- 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:
10.1090/S0002-9939-96-03525-3
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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