# Fungrim entry: 12b1d0

$R_D\!\left(-x, -y, z\right) = -\overline{i R_D\!\left(x, y, -z\right)}$
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_D\!\left(-x, -y, z\right) = -\overline{i R_D\!\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
CarlsonRD$R_D\!\left(x, y, z\right)$ Degenerate Carlson symmetric elliptic integral of the third kind
Conjugate$\overline{z}$ Complex conjugate
ConstI$i$ Imaginary unit
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("12b1d0"),
Formula(Equal(CarlsonRD(Neg(x), Neg(y), z), Neg(Conjugate(Mul(ConstI, CarlsonRD(x, y, Neg(z))))))),
Variables(x, y, z),
Assumptions(And(Element(x, OpenClosedInterval(0, Infinity)), Element(y, OpenClosedInterval(0, Infinity)), Element(z, OpenClosedInterval(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