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Fungrim entry: f6b4a2

RJ ⁣(0,x,x,w)=3π2(xw+wx)R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}
Assumptions:xC  and  wC  and  (x(,0)  or  Im(w)0)x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)
R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)
Fungrim symbol Notation Short description
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) Carlson symmetric elliptic integral of the third kind
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
ImIm(z)\operatorname{Im}(z) Imaginary part
Source code for this entry:
    Formula(Equal(CarlsonRJ(0, x, x, w), Div(Mul(3, Pi), Mul(2, Add(Mul(x, Sqrt(w)), Mul(w, Sqrt(x))))))),
    Variables(x, w),
    Assumptions(And(Element(x, CC), Element(w, CC), Or(NotElement(x, OpenInterval(Neg(Infinity), 0)), GreaterEqual(Im(w), 0)))))

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2021-03-15 19:12:00.328586 UTC