# Fungrim entry: 62b0c4

$R_J\!\left(0, -1, 1, 1\right) = \frac{3 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} \left(1 - i\right) - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}} \left(1 + i\right)$
TeX:
R_J\!\left(0, -1, 1, 1\right) = \frac{3 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} \left(1 - i\right) - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}} \left(1 + i\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Pow${a}^{b}$ Power
Gamma$\Gamma(z)$ Gamma function
Sqrt$\sqrt{z}$ Principal square root
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
Source code for this entry:
Entry(ID("62b0c4"),
Formula(Equal(CarlsonRJ(0, -1, 1, 1), Sub(Mul(Div(Mul(3, Pow(Gamma(Div(1, 4)), 2)), Mul(8, Sqrt(Mul(2, Pi)))), Sub(1, ConstI)), Mul(Div(Mul(Mul(3, Sqrt(2)), Pow(Pi, Div(3, 2))), Mul(2, Pow(Gamma(Div(1, 4)), 2))), Add(1, ConstI))))))

## Topics using this entry

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