Fungrim entry: 3047b1

R_D\!\left(1, -1, -1\right) = -\frac{3}{4} - \frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{8} + \frac{3 \sqrt{2} \pi i}{16}

TeX:

R_D\!\left(1, -1, -1\right) = -\frac{3}{4} - \frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{8} + \frac{3 \sqrt{2} \pi i}{16}

Definitions:

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

Source code for this entry:

Entry(ID("3047b1"),
    Formula(Equal(CarlsonRD(1, -1, -1), Add(Sub(Neg(Div(3, 4)), Div(Mul(Mul(3, Sqrt(2)), Log(Add(1, Sqrt(2)))), 8)), Div(Mul(Mul(Mul(3, Sqrt(2)), Pi), ConstI), 16)))))

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