# Fungrim entry: 9673f7

$R_D\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_D\!\left(x + \varepsilon i, y + \varepsilon i, z + \varepsilon i\right)$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)$
TeX:
R_D\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_D\!\left(x + \varepsilon i, y + \varepsilon i, z + \varepsilon i\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRD$R_D\!\left(x, y, z\right)$ Degenerate Carlson symmetric elliptic integral of the third kind
RightLimit$\lim_{x \to {a}^{+}} f(x)$ Limiting value, from the right
ConstI$i$ Imaginary unit
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("9673f7"),
Variables(x, y, z),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, SetMinus(CC, Set(0))), Or(NotEqual(x, 0), NotEqual(y, 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