Fungrim entry: f07e9d

R_D\!\left(0, 0, z\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{{z}^{3 / 2}}\right) \infty, & z \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

Assumptions:

z \in \mathbb{C}

TeX:

R_D\!\left(0, 0, z\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{{z}^{3 / 2}}\right) \infty, & z \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind
`Sign`	$\operatorname{sgn}(z)$	Sign function
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f07e9d"),
    Formula(Equal(CarlsonRD(0, 0, z), Cases(Tuple(Mul(Sign(Div(1, Pow(z, Div(3, 2)))), Infinity), NotEqual(z, 0)), Tuple(UnsignedInfinity, Otherwise)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals