Fungrim entry: f9b773

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:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

TeX:

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}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`RightLimit`	$\lim_{x \to {a}^{+}} f(x)$	Limiting value, from the right
`ConstI`	$i$	Imaginary unit
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f9b773"),
    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))))

Topics using this entry

Carlson symmetric elliptic integrals