Some infinite series
HTML articles powered by AMS MathViewer
- by H. F. Sandham PDF
- Proc. Amer. Math. Soc. 5 (1954), 430-436 Request permission
References
-
S. Ramanujan, Collected papers of Srinivasa Ramanujan, Cambridge, 1927. The series (1.41), (1.42), (1.12) are theorems (4), (5), (6), page xxxv, and the series (3.22), (6.221) are questions 358, 387, page 326. Although he only stated some particular cases there is no doubt that all the general formulae of this paper were known to Ramanujan. Those familiar with his work will recall his preference for stating most interesting particular cases rather than writing out general formulae. Other proofs of some of these series have been given:
G. N. Watson, J. London Math. Soc. vol. 3 (1928) pp. 216-225.
G. H. Hardy, J. London Math. Soc. vol. 3 (1928) pp. 238-240.
- H. F. Sandham, Three summations due to Ramanujan, Quart. J. Math. Oxford Ser. (2) 1 (1950), 238–240. MR 38450, DOI 10.1093/qmath/1.1.238
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 5 (1954), 430-436
- MSC: Primary 40.0X
- DOI: https://doi.org/10.1090/S0002-9939-1954-0062248-X
- MathSciNet review: 0062248