# Fungrim entry: 0ed5e2

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

x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first 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("0ed5e2"),
Formula(Equal(CarlsonRF(0, x, Mul(2, x)), Mul(Div(1, Sqrt(x)), Div(Pow(Gamma(Div(1, 4)), 2), Mul(4, Sqrt(Mul(2, Pi))))))),
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