# Fungrim entry: 415ff0

$R_F\!\left(0, x, y\right) = \frac{K\!\left(1 - \frac{y}{x}\right)}{\sqrt{x}}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi$
TeX:
R_F\!\left(0, x, y\right) = \frac{K\!\left(1 - \frac{y}{x}\right)}{\sqrt{x}}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi
Definitions:
Fungrim symbol Notation Short description
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first kind
EllipticK$K(m)$ Legendre complete elliptic integral of the first kind
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Abs$\left|z\right|$ Absolute value
Arg$\arg(z)$ Complex argument
Pi$\pi$ The constant pi (3.14...)
Source code for this entry:
Entry(ID("415ff0"),
Formula(Equal(CarlsonRF(0, x, y), Div(EllipticK(Sub(1, Div(y, x))), Sqrt(x)))),
Variables(x, y),
Assumptions(And(Element(x, CC), Element(y, CC), Less(Abs(Sub(Arg(x), Arg(y))), Pi))))

## 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