Fungrim entry: 9f3474

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

TeX:

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

Definitions:

Fungrim symbol	Notation	Short description
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second 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("9f3474"),
    Formula(Equal(EllipticE(-1), Mul(Sqrt(2), Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(8, Sqrt(Pi))), Div(Pow(Pi, Div(3, 2)), Pow(Gamma(Div(1, 4)), 2)))))))

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