충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권4호
  • /
  • Pages.277-295
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  • 2022
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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A FEW CLASSES OF INFINITE SERIES IDENTITIES FROM A MODULAR TRANSFORMATION FORMULA

  • Lim, Sung Geun (Department of Mathematics Education Mokwon University)
  • 투고 : 2022.06.13
  • 심사 : 2022.10.25
  • 발행 : 2022.11.30
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초록

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

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참고문헌

  1. G. E. Andrews, R. Askey and R. Roy, Special functions, Cambridge University Press, 1999.
  2. B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, The Rocky mountain J. Math., 7 (1977), no. 1, 147-189.
  3. B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Fur die reine und angewandte Math., 304 (1978), 332-365.
  4. S. Lim, Modular transformation formulae for generalized non-holomorphic Eisenstein series, Honam Math. J., 35 (2013), no. 3, 507-513. https://doi.org/10.5831/HMJ.2013.35.3.507
  5. S. Lim, Series relations coming from certain functions related to generalized non-holomorhic Eisenstein series, J. Chungcheong Math. Soc., 34 (2021), no. 2, 139-155. https://doi.org/10.14403/JCMS.2021.34.2.139
  6. S. Lim, Infinite series identities which stem from generalized non-holomorphic Eisenstein series, J. Chungcheong Math. Soc., 32 (2019), no. 4, 421-440. https://doi.org/10.14403/JCMS.2019.32.4.421
  7. S. Ramanujan, Notebooks of Srinivasa Ramanujan (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.