# Fungrim entry: 3f1547

$R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)$
Assumptions:$x \in \mathbb{C}$
TeX:
R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)

x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRG$R_G\!\left(x, y, z\right)$ Carlson symmetric 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...)
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("3f1547"),
Formula(Equal(CarlsonRG(0, x, Mul(2, x)), Mul(Sqrt(x), Mul(Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(8, Sqrt(Mul(2, Pi)))), Div(Pow(Pi, Div(3, 2)), Mul(Sqrt(2), Pow(Gamma(Div(1, 4)), 2)))))))),
Variables(x),
Assumptions(Element(x, CC)))

## 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