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# Fungrim entry: 0a2120

$E_{2 k}\!\left(\tau\right) = \frac{G_{2 k}\!\left(\tau\right)}{2 \zeta\!\left(2 k\right)}$
Assumptions:$k \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
E_{2 k}\!\left(\tau\right) = \frac{G_{2 k}\!\left(\tau\right)}{2 \zeta\!\left(2 k\right)}

k \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
EisensteinE$E_{k}\!\left(\tau\right)$ Normalized Eisenstein series
EisensteinG$G_{k}\!\left(\tau\right)$ Eisenstein series
RiemannZeta$\zeta(s)$ Riemann zeta function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("0a2120"),
Formula(Equal(EisensteinE(Mul(2, k), tau), Div(EisensteinG(Mul(2, k), tau), Mul(2, RiemannZeta(Mul(2, k)))))),
Variables(k, tau),
Assumptions(And(Element(k, ZZGreaterEqual(1)), Element(tau, HH))))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC