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Fungrim entry: 7a9dad

atan ⁣(xy)=xRC ⁣(y2,y2+x2)\operatorname{atan}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2}, {y}^{2} + {x}^{2}\right)
Assumptions:y(0,)  and  xRy \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
\operatorname{atan}\!\left(\frac{x}{y}\right) = x R_C\!\left({y}^{2}, {y}^{2} + {x}^{2}\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
Fungrim symbol Notation Short description
Atanatan(z)\operatorname{atan}(z) Inverse tangent
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
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(Equal(Atan(Div(x, y)), Mul(x, CarlsonRC(Pow(y, 2), Add(Pow(y, 2), Pow(x, 2)))))),
    Variables(x, y),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(x, RR))))

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2021-03-15 19:12:00.328586 UTC