Korean J. Math. Vol. 30 No. 1 (2022) pp.25-42
DOI: https://doi.org/10.11568/kjm.2022.30.1.25

Character analogues of infinite series identities related to generalized non-holomorphic Eisenstein series

Article Sidebar

PDF
Published: Mar 30, 2022
Keywords:
Character analogues, Infinite series identities, Modular transformation
Mathematics Subject Classification:
11F12, 34A25

Main Article Content

Sung-Geun Lim
Department of Mathematics Education, Mokwon University, Daejun 35349, Korea

Abstract

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



Article Details

References

[1] G. E. Andrews, R. Askey, R. Roy, Special functions, Cambridge University Press, 1999. Google Scholar

[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. Google Scholar

[3] S. Lim, Character analogues of infinite series from a certain modular transformation formula, J. Korean. Math. Soc. 48 (1) (2011), 169–178. Google Scholar

[4] S. Lim, Analytic continuation of generalized non-holomorphic Eisenstein series, Korean J. Math. 21 (3) (2013) 285–292. Google Scholar

[5] S. Lim, Infinite series identities which stem from generalized non-holomorphic Eisenstein series, J. Chungcheong Math. Soc. 32 (4) (2019), 421–440. Google Scholar

[6] L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, 1960. Google Scholar