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Proceedings of the American Mathematical Society

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Some infinite series


Author: H. F. Sandham
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
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  • [1] 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:
  • [2] G. N. Watson, J. London Math. Soc. vol. 3 (1928) pp. 216-225.
  • [3] G. H. Hardy, J. London Math. Soc. vol. 3 (1928) pp. 238-240.
  • [4] H. F. Sandham, Three summations due to Ramanujan, Quart. J. Math., Oxford Ser. (2) 1 (1950), 238–240. MR 0038450, https://doi.org/10.1093/qmath/1.1.238

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DOI: https://doi.org/10.1090/S0002-9939-1954-0062248-X
Article copyright: © Copyright 1954 American Mathematical Society