Fungrim entry: 6c71c0

E_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{27 {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{512 {\pi}^{12}}

TeX:

E_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{27 {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{512 {\pi}^{12}}

Definitions:

Fungrim symbol	Notation	Short description
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function

Source code for this entry:

Entry(ID("6c71c0"),
    Formula(Equal(EisensteinE(6, Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), Div(Mul(27, Pow(Gamma(Div(1, 3)), 18)), Mul(512, Pow(Pi, 12))))))

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