Fungrim entry: 423b36

\operatorname{asinh}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2} + {x}^{2}, {y}^{2}\right)

Assumptions:

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}

TeX:

\operatorname{asinh}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2} + {x}^{2}, {y}^{2}\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`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
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("423b36"),
    Formula(Equal(Asinh(Div(x, y)), Mul(x, CarlsonRC(Add(Pow(y, 2), Pow(x, 2)), Pow(y, 2))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, RR))))

Topics using this entry

Carlson symmetric elliptic integrals

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