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

Carlson symmetric elliptic integrals