Korean Journal of Mathematics

  • 제30권1호
  • /
  • Pages.25-42
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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CHARACTER ANALOGUES OF INFINITE SERIES IDENTITIES RELATED TO GENERALIZED NON-HOLOMORPHIC EISENSTEIN SERIES

  • Lim, Sung Geun (Department of Mathematics Education, Mokwon University)
  • 투고 : 2021.05.04
  • 심사 : 2022.01.04
  • 발행 : 2022.03.30
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초록

In this paper, we derive analogues of a couple of classes of infinite series identities with the confluent hypergeometric functions involving Dirichlet characters.

키워드

참고문헌

  1. G. E. Andrews, R. Askey, R. Roy, Special functions, Cambridge University Press, 1999.
  2. B. C. Berndt, A. Dixit, J. Sohn Character analogues of theorems of Ramanujan, Koshliakov and Guinand, Adv. in Appl. Math. 46 (1) (2011), 54-70. https://doi.org/10.1016/j.aam.2009.12.003
  3. S. Lim, Character analogues of infinite series from a certain modular transformation formula, J. Korean. Math. Soc. 48 (1) (2011), 169-178. https://doi.org/10.4134/JKMS.2011.48.1.169
  4. 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
  5. S. Lim, Infinite series identities which stem from generalized non-holomorphic Eisenstein series, J. Chungcheong Math. Soc. 32 (4) (2019), 421-440. https://doi.org/10.14403/JCMS.2019.32.4.421
  6. L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, 1960.