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http://dx.doi.org/10.5831/HMJ.2016.38.3.479

ON SOME SERIES IDENTITIES  

Lim, Sung-Geun (Department of Mathematics Education, Mokwon University)
Publication Information
Honam Mathematical Journal / v.38, no.3, 2016 , pp. 479-494 More about this Journal
Abstract
In this paper, using a transformation formula for a certain series which comes from the generalized non-analytic Eisenstein series, we obtained some infinite series identities which contain Ramanujan's formula and author's previous results.
Keywords
Infinite series identities; non-analytic Eisenstein series; modular transformation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 B. C. Berndt, Generalized Eisenstein series and modihied Dedekind sums, J. Reine. Angew. Math. 272 (1975), 182-193.
2 B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, The Rocky mountain J. Math. 7(1) (1977), 147-189.   DOI
3 B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine. Angew. Math. 304 (1978), 332-365.
4 Y. Komori, K. Matsumoto and H. Tsumura, Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions, preprint.
5 S. Lim, Infinite series Identities from modular transformation formulas that stem from generalized Eisenstein series, Acta Arith. 141(3) (2010), 241-273.   DOI
6 S. Lim, Analytic continuation of generalized non-holomorphic Eisenstein series, Korean J. Math. 21(3) (2013), 285-292.   DOI
7 S. L. Malurkar, On the application of Herr Mellin's integrals to some series, J. Indian Math. Soc. 16 (1925-1926), 130-138.
8 S. Ramanujan, Notebooks of Srinivasa Ramanujan (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
9 L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, 1960.
10 E. C. Titchmarsh, Theory of functions, Oxford University Press, 1952.