Browse > Article
http://dx.doi.org/10.14403/jcms.2019.32.4.421

INFINITE SERIES IDENTITIES WHICH STEM FROM GENERALIZED NON-HOLOMORPHIC EISENSTEIN SERIES  

Lim, Sung-Geun (Department of Mathematics Education Mokwon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.32, no.4, 2019 , pp. 421-440 More about this Journal
Abstract
We establish a few class of infinite series identities from modular transformation formulas for certain series which originally come from generalized non-holomorphic Eisenstein series.
Keywords
Infinite series; Modular transformation; non-holomorphic Eisenstein series;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, The Rocky mountain J. Math., 7 (1977), no 1, 147-189.   DOI
2 B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine. Angew. Math., 304 (1978), 332-365.
3 S. Lim, Infinite series Identities from modular transformation formulas that stem from generalized Eisenstein series, Acta Arith., 141 (2010), no 3, 241-273.   DOI
4 S. Lim, Analytic continuation of generalized non-holomorphic Eisenstein series, Korean J. Math., 21 (2013), no. 3, 285-292.   DOI
5 S. Lim, On some series identities, Honam Mathematical J., 38 (2016), no. 3, 479-494.   DOI
6 L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, 1960.
7 L. Lewin, Polylogarithms and Associated functions, New York, 1981.