Note on the Bradley and Ramanujan summation
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- by Chu Wenchang PDF
- Proc. Amer. Math. Soc. 124 (1996), 3753-3754 Request permission
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
- W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.
- David Bradley, On a claim of Ramanujan about certain hypergeometric series, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1145–1149. MR 1189537, DOI 10.1090/S0002-9939-1994-1189537-5
- Wen Chang Chu, Inversion techniques and combinatorial identities, Boll. Un. Mat. Ital. B (7) 7 (1993), no. 4, 737–760 (English, with Italian summary). MR 1255645
- W. C. Chu and L. C. Hsu, Some new applications of Gould-Hsu inversion, J. Combin. Inform. System Sci. 14 (1989), no. 1, 1–4. MR 1068649
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
Additional Information
- Chu Wenchang
- Affiliation: Istituto di Matematica, “Guido Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Roma, Italia
- MR Author ID: 213991
- Email: WENCHANG@mat.uniroma1.it
- 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 1996 American Mathematical Society
- 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