Fungrim entry: 361801

\operatorname{agm}\!\left(1, 3 + 2 \sqrt{2}\right) = \frac{2 \left(2 + \sqrt{2}\right) {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}

TeX:

\operatorname{agm}\!\left(1, 3 + 2 \sqrt{2}\right) = \frac{2 \left(2 + \sqrt{2}\right) {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Gamma`	$\Gamma(z)$	Gamma function

Source code for this entry:

Entry(ID("361801"),
    Formula(Equal(AGM(1, Add(3, Mul(2, Sqrt(2)))), Div(Mul(2, Add(2, Sqrt(2)), Pow(Pi, Div(3, 2))), Pow(Gamma(Div(1, 4)), 2)))))

Topics using this entry

Arithmetic-geometric mean

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