Fungrim entry: 0d3186

R_F\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_F\!\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} \;\mathbin{\operatorname{and}}\; \left(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)

TeX:

R_F\!\left(x, y, z\right) = \lim_{\varepsilon \to {0}^{+}} R_F\!\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} \;\mathbin{\operatorname{and}}\; \left(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	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("0d3186"),
    Formula(Equal(CarlsonRF(x, y, z), RightLimit(CarlsonRF(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), Or(And(NotEqual(x, 0), NotEqual(y, 0)), And(NotEqual(x, 0), NotEqual(z, 0)), And(NotEqual(y, 0), NotEqual(z, 0))))))

Topics using this entry

Carlson symmetric elliptic integrals