Fungrim entry: 05a3ee

Symbol: ComplexLimit —

\lim_{z \to a} f\!\left(z\right)

— Limiting value, complex variable

This operator can be called with three or four arguments.

ComplexLimit(f(z), z, a), rendered as

\lim_{z \to a} f\!\left(z\right)

, is equivalent to Limit(f(z), z, a, Element(z, CC)) but renders to LaTeX without displaying the predicate

z \in \mathbb{C}

which readers will typically understand from context.

ComplexLimit(f(z), z, a, P(z)), rendered as

\lim_{z \to a, P\left(z\right)} f\!\left(z\right)

, is equivalent to Limit(f(z), z, a, And(Element(z, CC), P(z))).

Definitions:

Fungrim symbol	Notation	Short description
`ComplexLimit`	$\lim_{z \to a} f\!\left(z\right)$	Limiting value, complex variable
`Limit`	$\lim_{x \to a} f\!\left(x\right)$	Limiting value
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("05a3ee"),
    SymbolDefinition(ComplexLimit, ComplexLimit(f(z), z, a), "Limiting value, complex variable"),
    Description("This operator can be called with three or four arguments."),
    Description(SourceForm(ComplexLimit(f(z), z, a)), ", rendered as", ComplexLimit(f(z), z, a), ", is equivalent to", SourceForm(Limit(f(z), z, a, Element(z, CC))), "but renders to LaTeX without displaying the predicate", Element(z, CC), " which readers will typically understand from context."),
    Description(SourceForm(ComplexLimit(f(z), z, a, P(z))), ", rendered as", ComplexLimit(f(z), z, a, P(z)), ", is equivalent to", SourceForm(Limit(f(z), z, a, And(Element(z, CC), P(z)))), "."))

Topics using this entry

Operators