Fungrim entry: 4b040d

K\!\left(\frac{4 - 3 \sqrt{2}}{8}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \cdot {2}^{1 / 4} \sqrt{\pi}}

TeX:

K\!\left(\frac{4 - 3 \sqrt{2}}{8}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \cdot  {2}^{1 / 4} \sqrt{\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("4b040d"),
    Formula(Equal(EllipticK(Div(Sub(4, Mul(3, Sqrt(2))), 8)), Div(Pow(Gamma(Div(1, 4)), 2), Mul(Mul(4, Pow(2, Div(1, 4))), Sqrt(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