Fungrim entry: 997777

G = \frac{{\pi}^{2}}{16} + \frac{\pi \log(2)}{4} - \int_{0}^{1} {\left(\operatorname{atan}(x)\right)}^{2} \, dx

TeX:

G = \frac{{\pi}^{2}}{16} + \frac{\pi \log(2)}{4} - \int_{0}^{1} {\left(\operatorname{atan}(x)\right)}^{2} \, dx

Definitions:

Fungrim symbol	Notation	Short description
`ConstCatalan`	$G$	Catalan's constant
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Log`	$\log(z)$	Natural logarithm
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Atan`	$\operatorname{atan}(z)$	Inverse tangent

Source code for this entry:

Entry(ID("997777"),
    Formula(Equal(ConstCatalan, Sub(Add(Div(Pow(Pi, 2), 16), Div(Mul(Pi, Log(2)), 4)), Integral(Pow(Atan(x), 2), For(x, 0, 1))))))

Topics using this entry

Catalan's constant

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