# Fungrim entry: fda084

$R_G\!\left(x, y, z\right) = R_{1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[x, y, z\right]\right)$
Assumptions:$x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right)$
TeX:
R_G\!\left(x, y, z\right) = R_{1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[x, y, z\right]\right)

x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRG$R_G\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the second kind
CarlsonHypergeometricR$R_{-a}\!\left(b, z\right)$ Carlson multivariate hypergeometric function
CC$\mathbb{C}$ Complex numbers
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("fda084"),
Formula(Equal(CarlsonRG(x, y, z), CarlsonHypergeometricR(Div(1, 2), List(Div(1, 2), Div(1, 2), Div(1, 2)), List(x, y, z)))),
Variables(x, y, z),
Assumptions(And(Element(x, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenInterval(Neg(Infinity), 0))))))

## 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