Fungrim entry: e1a3cb

R_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C}

TeX:

R_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	Carlson symmetric elliptic integral of the third kind
`Sign`	$\operatorname{sgn}(z)$	Sign function
`Sqrt`	$\sqrt{z}$	Principal square root
`Infinity`	$\infty$	Positive infinity
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("e1a3cb"),
    Formula(Equal(CarlsonRJ(0, 0, z, w), Cases(Tuple(Mul(Sign(Div(1, Mul(Sqrt(z), w))), Infinity), And(NotEqual(z, 0), NotEqual(w, 0))), Tuple(UnsignedInfinity, Otherwise)))),
    Variables(z, w),
    Assumptions(And(Element(z, CC), Element(w, CC))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals