Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON SOME SERIES IDENTITIES

  • Lim, Sung-Geun (Department of Mathematics Education, Mokwon University)
  • Received : 2016.04.05
  • Accepted : 2016.06.01
  • Published : 2016.09.25
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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.

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References

  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. https://doi.org/10.1216/RMJ-1977-7-1-147
  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. https://doi.org/10.4064/aa141-3-2
  6. S. Lim, Analytic continuation of generalized non-holomorphic Eisenstein series, Korean J. Math. 21(3) (2013), 285-292. https://doi.org/10.11568/kjm.2013.21.3.285
  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.