Fungrim entry: dbf388

G_{2}\!\left(\tau\right) = -4 \pi i \frac{\eta'(\tau)}{\eta(\tau)}

Assumptions:

\tau \in \mathbb{H}

TeX:

G_{2}\!\left(\tau\right) = -4 \pi i \frac{\eta'(\tau)}{\eta(\tau)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`EisensteinG`	$G_{k}\!\left(\tau\right)$	Eisenstein series
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("dbf388"),
    Formula(Equal(EisensteinG(2, tau), Neg(Mul(Mul(Mul(4, Pi), ConstI), Div(ComplexDerivative(DedekindEta(tau), For(tau, tau)), DedekindEta(tau)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Eisenstein series

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

2021-03-15 19:12:00.328586 UTC