# Fungrim entry: f6b4a2

$R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)$
TeX:
R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Pi$\pi$ The constant pi (3.14...)
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Im$\operatorname{Im}(z)$ Imaginary part
Source code for this entry:
Entry(ID("f6b4a2"),
Formula(Equal(CarlsonRJ(0, x, x, w), Div(Mul(3, Pi), Mul(2, Add(Mul(x, Sqrt(w)), Mul(w, Sqrt(x))))))),
Variables(x, w),
Assumptions(And(Element(x, CC), Element(w, CC), Or(NotElement(x, OpenInterval(Neg(Infinity), 0)), GreaterEqual(Im(w), 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