Fungrim symbol: Arg

Symbol: Arg —

\arg(z)

— Complex argument

Domain	Codomain
$z \in \mathbb{R}$	$\arg(z) \in \left\{0, \pi\right\}$
$z \in \mathbb{C}$	$\arg(z) \in \left(-\pi, \pi\right]$
$z \in \left\{\infty\right\}$	$\arg(z) \in \left\{0\right\}$
$z \in \left\{-\infty\right\}$	$\arg(z) \in \left\{\pi\right\}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`Arg`	$\arg(z)$	Complex argument
`RR`	$\mathbb{R}$	Real numbers
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("b7d740"),
    SymbolDefinition(Arg, Arg(z), "Complex argument"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Arg(z), Set(0, Pi))), Tuple(Element(z, CC), Element(Arg(z), OpenClosedInterval(Neg(Pi), Pi))), Tuple(Element(z, Set(Infinity)), Element(Arg(z), Set(0))), Tuple(Element(z, Set(Neg(Infinity))), Element(Arg(z), Set(Pi))))))

Topics using this symbol

The symbol Arg appears in 11 topics:

Complex parts (in 10 entries)
Powers (in 5 entries)
Square roots (in 4 entries)
Specific values of Carlson symmetric elliptic integrals (in 4 entries)
Carlson symmetric elliptic integrals (in 4 entries)
Natural logarithm (in 3 entries)
Imaginary unit (in 2 entries)
Arithmetic-geometric mean (in 2 entries)
Series representations of Carlson symmetric elliptic integrals (in 1 entries)
Exponential function (in 1 entries)
Barnes G-function (in 1 entries)

Entries using this symbol

The symbol Arg appears in 31 entries: