Fungrim entry: b95ffa

K\!\left(4 \sqrt{3} - 7\right) = \frac{\sqrt{3 + 2 \sqrt{3}} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3}}{{2}^{10 / 3} \pi}

TeX:

K\!\left(4 \sqrt{3} - 7\right) = \frac{\sqrt{3 + 2 \sqrt{3}} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3}}{{2}^{10 / 3} \pi}

Definitions:

Fungrim symbol	Notation	Short description
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("b95ffa"),
    Formula(Equal(EllipticK(Sub(Mul(4, Sqrt(3)), 7)), Div(Mul(Sqrt(Add(3, Mul(2, Sqrt(3)))), Pow(Gamma(Div(1, 3)), 3)), Mul(Pow(2, Div(10, 3)), Pi)))))

Topics using this entry

Legendre elliptic integrals

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