Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2020; 35(1): 63-81

Online first article December 27, 2019      Printed January 31, 2020

https://doi.org/10.4134/CKMS.c180528

Copyright © The Korean Mathematical Society.

Identities about level 2 Eisenstein series

Ce Xu

Xiamen University

Abstract

In this paper we consider certain classes of generalized level 2 Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formulas for some level 2 Eisenstein series. We can find that these level 2 Eisenstein series are reducible to infinite series involving hyperbolic functions. Moreover, some interesting new examples are given.

Keywords: Eisenstein series, trigonometric function, hyperbolic function, Gamma function

MSC numbers: 11M41, 11M99