# Fungrim entry: 398bb7

$\log\!\left(\frac{x}{y}\right) = \left(x - y\right) R_C\!\left(\frac{{\left(x + y\right)}^{2}}{4}, x y\right)$
Assumptions:$y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)$
TeX:
\log\!\left(\frac{x}{y}\right) = \left(x - y\right) R_C\!\left(\frac{{\left(x + y\right)}^{2}}{4}, x y\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Log$\log(z)$ Natural logarithm
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
Pow${a}^{b}$ Power
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("398bb7"),
Formula(Equal(Log(Div(x, y)), Mul(Sub(x, y), CarlsonRC(Div(Pow(Add(x, y), 2), 4), Mul(x, y))))),
Variables(x, y),
Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, OpenInterval(0, Infinity)))))

## 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