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Fungrim entry: 6923d5

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

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first 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(CarlsonRC(x, y), RightLimit(CarlsonRC(Add(x, Mul(epsilon, ConstI)), Add(y, Mul(epsilon, ConstI))), For(epsilon, 0)))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, SetMinus(CC, Set(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