Fungrim entry: 6923d5

R_C\!\left(x, y\right) = \lim_{\varepsilon \to {0}^{+}} R_C\!\left(x + \varepsilon i, y + \varepsilon i\right)

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left\{0\right\}

TeX:

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\}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRC`	$R_C\!\left(x, y\right)$	Degenerate Carlson symmetric elliptic integral of the first 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("6923d5"),
    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))))))

Topics using this entry

Carlson symmetric elliptic integrals