# Fungrim entry: 120284

$R_G\!\left(x, x, y\right) = \frac{1}{2} \begin{cases} x R_C\!\left(y, x\right) + \sqrt{y}, & x \ne 0\\\sqrt{y}, & x = 0\\ \end{cases}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}$
TeX:
R_G\!\left(x, x, y\right) = \frac{1}{2} \begin{cases} x R_C\!\left(y, x\right) + \sqrt{y}, & x \ne 0\\\sqrt{y}, & x = 0\\ \end{cases}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRG$R_G\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the second kind
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("120284"),
Formula(Equal(CarlsonRG(x, x, y), Mul(Div(1, 2), Cases(Tuple(Add(Mul(x, CarlsonRC(y, x)), Sqrt(y)), NotEqual(x, 0)), Tuple(Sqrt(y), Equal(x, 0)))))),
Variables(x, y),
Assumptions(And(Element(x, CC), Element(y, CC))))

## 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