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Fungrim entry: 33e034

acos ⁣(xy)=y2x2RC ⁣(x2,y2)\operatorname{acos}\!\left(\frac{x}{y}\right) = \sqrt{{y}^{2} - {x}^{2}} R_C\!\left({x}^{2}, {y}^{2}\right)
Assumptions:y(0,)  and  x[0,y]y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left[0, y\right]
TeX:
\operatorname{acos}\!\left(\frac{x}{y}\right) = \sqrt{{y}^{2} - {x}^{2}} R_C\!\left({x}^{2}, {y}^{2}\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left[0, y\right]
Definitions:
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
ClosedInterval[a,b]\left[a, b\right] Closed interval
Source code for this entry:
Entry(ID("33e034"),
    Formula(Equal(Acos(Div(x, y)), Mul(Sqrt(Sub(Pow(y, 2), Pow(x, 2))), CarlsonRC(Pow(x, 2), Pow(y, 2))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, ClosedInterval(0, y)))))

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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