Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME INFINITE SERIES IDENTITIES

  • Received : 2012.10.15
  • Accepted : 2012.12.15
  • Published : 2012.12.30
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Abstract

B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.

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References

  1. M. Abramowitz and I.A. Stegun, editor, Handbook of mathematical functions, New York 1965.
  2. B.C. Berndt, Generalized Dedekind eta-functions and generalized Dedekind sums, Trans. Amer. Math. Soc. 178 (1973), 495-508. https://doi.org/10.1090/S0002-9947-1973-0371817-5
  3. B.C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, Rocky mountain J. Math. 7 (1) (1977), 147-189. https://doi.org/10.1216/RMJ-1977-7-1-147
  4. B.C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine Angew. Math. 304 (1978), 332-365.
  5. J. Lagrange, Une formule sommatoire et ses applications, Bull. Sci. Math. (2) 84 (1960), 105-110.
  6. S. Ramanujan, Notebooks of Srinivasa Ramanujan (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
  7. O. Schlomilch, Ueber einige unendliche Reichen, Berichte uber die Verh. d. Konige Sachsischen Gesell. Wiss. zu Leipzig 29 (1877), 101-105.
  8. O. Schlomilch, Compendium der hoheren Analysis, Zweiter Band, 4th ed., Friedrich Vieweg und Sohn, Braunschweig, 1895.
  9. G.N. Watson, Theorems stated by Ramanujan II, J. Lond. Math. Soc. 3 (1928), 216-225. https://doi.org/10.1112/jlms/s1-3.3.216
  10. E.T. Whittaker and G. N. Watson, A course in modern analysis, 4th ed. Cambridge, England, 1990.