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Fungrim entry: 3e1435

ddxRG ⁣(x,y,z)+ddyRG ⁣(x,y,z)+ddzRG ⁣(x,y,z)=12RF ⁣(x,y,z)\frac{d}{d x}\, R_G\!\left(x, y, z\right) + \frac{d}{d y}\, R_G\!\left(x, y, z\right) + \frac{d}{d z}\, R_G\!\left(x, y, z\right) = \frac{1}{2} R_F\!\left(x, y, z\right)
Assumptions:xC(,0]  and  yC(,0]  and  zC(,0]x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]
x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Equal(Add(Add(ComplexDerivative(CarlsonRG(x, y, z), For(x, x)), ComplexDerivative(CarlsonRG(x, y, z), For(y, y))), ComplexDerivative(CarlsonRG(x, y, z), For(z, z))), Mul(Div(1, 2), CarlsonRF(x, y, z))),
    Variables(x, y, z),
    Assumptions(And(Element(x, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

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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