# Fungrim entry: d9765b

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

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left[y, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Source code for this entry:
Entry(ID("d9765b"),
Formula(Equal(Acosh(Div(x, y)), Mul(Sqrt(Sub(Pow(x, 2), Pow(y, 2))), CarlsonRC(Pow(x, 2), Pow(y, 2))))),
Variables(x, y),
Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, ClosedOpenInterval(y, 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