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Fungrim entry: d9765b

acosh ⁣(xy)=x2y2RC ⁣(x2,y2)\operatorname{acosh}\!\left(\frac{x}{y}\right) = \sqrt{{x}^{2} - {y}^{2}} R_C\!\left({x}^{2}, {y}^{2}\right)
Assumptions:y(0,)  and  x[y,)y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left[y, \infty\right)
\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)
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Source code for this entry:
    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)))))

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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