Fungrim entry: 7cbe17

R_C\!\left(x, 0\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{x}}\right) \infty, & x \ne 0\\{\tilde \infty}, & x = 0\\ \end{cases}

Assumptions:

x \in \mathbb{C}

TeX:

R_C\!\left(x, 0\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{x}}\right) \infty, & x \ne 0\\{\tilde \infty}, & x = 0\\ \end{cases}

x \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRC`	$R_C\!\left(x, y\right)$	Degenerate Carlson symmetric elliptic integral of the first 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("7cbe17"),
    Formula(Equal(CarlsonRC(x, 0), Cases(Tuple(Mul(Sign(Div(1, Sqrt(x))), Infinity), NotEqual(x, 0)), Tuple(UnsignedInfinity, Equal(x, 0))))),
    Variables(x),
    Assumptions(Element(x, CC)))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals