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Fungrim entry: bc2f88

RC ⁣(x,y)=1x+y(π2atanh ⁣(xx+y)i)R_C\!\left(-x, y\right) = \frac{1}{\sqrt{x + y}} \left(\frac{\pi}{2} - \operatorname{atanh}\!\left(\sqrt{\frac{x}{x + y}}\right) i\right)
Assumptions:x(0,)  and  y(0,)x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
R_C\!\left(-x, y\right) = \frac{1}{\sqrt{x + y}} \left(\frac{\pi}{2} - \operatorname{atanh}\!\left(\sqrt{\frac{x}{x + y}}\right) i\right)

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(CarlsonRC(Neg(x), y), Mul(Div(1, Sqrt(Add(x, y))), Sub(Div(Pi, 2), Mul(Atanh(Sqrt(Div(x, Add(x, y)))), ConstI))))),
    Variables(x, y),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)))))

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2021-03-15 19:12:00.328586 UTC