Fungrim home page

Fungrim entry: 871996

η(τ)=iπ12η(τ)E2 ⁣(τ)\eta'(\tau) = \frac{i \pi}{12} \eta(\tau) E_{2}\!\left(\tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta'(\tau) = \frac{i \pi}{12} \eta(\tau) E_{2}\!\left(\tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
ConstIii Imaginary unit
Piπ\pi The constant pi (3.14...)
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("871996"),
    Formula(Equal(ComplexDerivative(DedekindEta(tau), For(tau, tau)), Mul(Mul(Div(Mul(ConstI, Pi), 12), DedekindEta(tau)), EisensteinE(2, tau)))),
    Variables(tau),
    Assumptions(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.

2019-11-19 15:10:20.037976 UTC