Fungrim entry: d6703a

G = \frac{7 \zeta\!\left(3\right)}{4 \pi} + \frac{2}{\pi} \int_{0}^{1} \frac{{\left(\operatorname{atan}(x)\right)}^{2}}{x} \, dx

TeX:

G = \frac{7 \zeta\!\left(3\right)}{4 \pi} + \frac{2}{\pi} \int_{0}^{1} \frac{{\left(\operatorname{atan}(x)\right)}^{2}}{x} \, dx

Definitions:

Fungrim symbol	Notation	Short description
`ConstCatalan`	$G$	Catalan's constant
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`Pi`	$\pi$	The constant pi (3.14...)
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Pow`	${a}^{b}$	Power
`Atan`	$\operatorname{atan}(z)$	Inverse tangent

Source code for this entry:

Entry(ID("d6703a"),
    Formula(Equal(ConstCatalan, Add(Div(Mul(7, RiemannZeta(3)), Mul(4, Pi)), Mul(Div(2, Pi), Integral(Div(Pow(Atan(x), 2), x), 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