# Fungrim entry: df3334

Symbol: EisensteinE $E_{k}\!\left(\tau\right)$ Normalized Eisenstein series
The normalized Eisenstein series $E_{k}\!\left(\tau\right)$ is defined for even integers $k \ge 2$ and $\tau$ in the upper half-plane.
The functions $G_{k}\!\left(\tau\right)$ and $E_{k}\!\left(\tau\right)$ are the same up to a normalizing factor.
Definitions:
Fungrim symbol Notation Short description
EisensteinE$E_{k}\!\left(\tau\right)$ Normalized Eisenstein series
EisensteinG$G_{k}\!\left(\tau\right)$ Eisenstein series
Source code for this entry:
Entry(ID("df3334"),
SymbolDefinition(EisensteinE, EisensteinE(k, tau), "Normalized Eisenstein series"),
Description("The normalized Eisenstein series", EisensteinE(k, tau), "is defined for even integers", GreaterEqual(k, 2), "and", tau, "in the upper half-plane."),
Description("The functions", EisensteinG(k, tau), "and", EisensteinE(k, tau), "are the same up to a normalizing factor."))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC