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Fungrim entry: 9673f7

RD ⁣(x,y,z)=limε0+RD ⁣(x+εi,y+εi,z+εi)R_D\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_D\!\left(x + \varepsilon i, y + \varepsilon i, z + \varepsilon i\right)
Assumptions:xC  and  yC  and  zC{0}  and  (x0  or  y0)x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)
R_D\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_D\!\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} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)
Fungrim symbol Notation Short description
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third 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(CarlsonRD(x, y, z), RightLimit(CarlsonRD(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, SetMinus(CC, Set(0))), Or(NotEqual(x, 0), NotEqual(y, 0)))))

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2021-03-15 19:12:00.328586 UTC