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Fungrim entry: f9b773

RG ⁣(x,y,z)=limε0+RG ⁣(x+εi,y+εi,z+εi)R_G\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_G\!\left(x + \varepsilon i, y + \varepsilon i, z + \varepsilon i\right)
Assumptions:xC  and  yC  and  zCx \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
R_G\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_G\!\left(x + \varepsilon i, y + \varepsilon i, z + \varepsilon i\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Fungrim symbol Notation Short description
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
RightLimitlimxa+f(x)\lim_{x \to {a}^{+}} f(x) Limiting value, from the right
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(CarlsonRG(x, y, z), RightLimit(CarlsonRG(Add(x, Mul(epsilon, ConstI)), Add(y, Mul(epsilon, ConstI)), Add(z, Mul(epsilon, ConstI))), For(epsilon, 0)))),
    Variables(x, y, z),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC))))

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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