# Fungrim entry: b8ca70

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

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \left(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ 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("b8ca70"),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), Element(w, SetMinus(CC, Set(0))), Or(And(NotEqual(x, 0), NotEqual(y, 0)), And(NotEqual(x, 0), NotEqual(z, 0)), And(NotEqual(y, 0), NotEqual(z, 0))))))