Fungrim entry: 534335

R_J\!\left(1, 1, -1, -1\right) = -\frac{3 \sqrt{2} \pi}{8} + \left(\frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2}\right) i

TeX:

R_J\!\left(1, 1, -1, -1\right) = -\frac{3 \sqrt{2} \pi}{8} + \left(\frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2}\right) i

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	Carlson symmetric elliptic integral of the third kind
`Sqrt`	$\sqrt{z}$	Principal square root
`Pi`	$\pi$	The constant pi (3.14...)
`Log`	$\log(z)$	Natural logarithm
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("534335"),
    Formula(Equal(CarlsonRJ(1, 1, -1, -1), Add(Neg(Div(Mul(Mul(3, Sqrt(2)), Pi), 8)), Mul(Sub(Div(Mul(Mul(3, Sqrt(2)), Log(Add(1, Sqrt(2)))), 4), Div(3, 2)), ConstI)))))

Topics using this entry

Specific values of Carlson symmetric 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