Fungrim entry: 40a376

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

TeX:

K\!\left(\frac{1}{2} - \frac{\sqrt{3}}{4}\right) = \frac{{3}^{1 / 4} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3}}{4 \cdot  {2}^{1 / 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("40a376"),
    Formula(Equal(EllipticK(Sub(Div(1, 2), Div(Sqrt(3), 4))), Div(Mul(Pow(3, Div(1, 4)), Pow(Gamma(Div(1, 3)), 3)), Mul(Mul(4, Pow(2, Div(1, 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