Korean Journal of Mathematics

  • 제19권4호
  • /
  • Pages.465-480
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  • 2011
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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IDENTITIES ABOUT INFINITE SERIES CONTAINING HYPERBOLIC FUNCTIONS AND TRIGONOMETRIC FUNCTIONS

  • 투고 : 2011.11.05
  • 심사 : 2011.12.14
  • 발행 : 2011.12.30
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초록

B. C. Berndt established many identities about infinite series. In this paper, continuing his work, we find new identities about infinite series containing hyperbolic functions and trigonometric functions.

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참고문헌

  1. B.C. Berndt, Two new proofs of Lerch's functional equation, Proc. Amer. Math. Soc. 32 (1972), 403-408.
  2. 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
  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. 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
  5. S. Lim, Series relations from certain modular transformation formula, J. Chungcheong Math. Soc. 24 (3) (2011), 481-502.
  6. S. Ramanujan, Notebooks of Srinivasa Ramanujan (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.