# Fungrim entry: 4091ad

$R_G\!\left(-x, -y, z\right) = -\overline{i R_G\!\left(x, y, -z\right)}$
Assumptions:$x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)$
TeX:
R_G\!\left(-x, -y, z\right) = -\overline{i R_G\!\left(x, y, -z\right)}

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRG$R_G\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the second kind
Conjugate$\overline{z}$ Complex conjugate
ConstI$i$ Imaginary unit
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("4091ad"),
Formula(Equal(CarlsonRG(Neg(x), Neg(y), z), Neg(Conjugate(Mul(ConstI, CarlsonRG(x, y, Neg(z))))))),
Variables(x, y, z),
Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

## 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