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Fungrim entry: 584a61

asin ⁣(xy)=xRC ⁣(y2x2,y2)\operatorname{asin}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2} - {x}^{2}, {y}^{2}\right)
Assumptions:y(0,)  and  x[y,y]y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \left[-y, y\right]
\operatorname{asin}\!\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 \left[-y, y\right]
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Powab{a}^{b} Power
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:
    Formula(Equal(Asin(Div(x, y)), Mul(x, CarlsonRC(Sub(Pow(y, 2), Pow(x, 2)), Pow(y, 2))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, ClosedInterval(Neg(y), y)))))

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2021-03-15 19:12:00.328586 UTC