Some infinite series identities

Ford, Kevin B.

doi:10.1090/S0002-9939-1993-1174491-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Some infinite series identities
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by Kevin B. Ford PDF

Proc. Amer. Math. Soc. 119 (1993), 1019-1020 Request permission

Abstract:

Certain infinite series are shown to satisfy simple identities between the square of the sum of the series and the sum of the squares of the terms of the series. The main tool is Ramanujan’s ${}_1{\psi _1}$ summation formula.

References

Bruce C. Berndt, Ramanujan’s notebooks. Part III, Springer-Verlag, New York, 1991. MR 1117903, DOI 10.1007/978-1-4612-0965-2
Mourad E. H. Ismail, A simple proof of Ramanujan’s $_{1}\psi _{1}$ sum, Proc. Amer. Math. Soc. 63 (1977), no. 1, 185–186. MR 508183, DOI 10.1090/S0002-9939-1977-0508183-7
Srinivasa Ramanujan, Notebooks. Vols. 1, 2, Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904