Identities about level 2 Eisenstein series
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 63-81
https://doi.org/10.4134/CKMS.c180528
Published online January 31, 2020
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
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