Fungrim entry: 05a3ee

Symbol: ComplexLimit —

\lim_{z \to a} f(z)

— Limiting value, complex variable

This operator can be called with three or four arguments.

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

\lim_{z \to a} f(z)

, is equivalent to Limit(f(z), For(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), For(z, a), P(z)), rendered as

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

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

The expression For(z, a) declares z as a locally bound variable within the scope of the arguments to this operator.

Definitions:

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

Source code for this entry:

Entry(ID("05a3ee"),
    SymbolDefinition(ComplexLimit, ComplexLimit(f(z), For(z, a)), "Limiting value, complex variable"),
    Description("This operator can be called with three or four arguments."),
    Description(SourceForm(ComplexLimit(f(z), For(z, a))), ", rendered as", ComplexLimit(f(z), For(z, a)), ", is equivalent to", SourceForm(Limit(f(z), For(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), For(z, a), P(z))), ", rendered as", ComplexLimit(f(z), For(z, a), P(z)), ", is equivalent to", SourceForm(Limit(f(z), For(z, a), And(Element(z, CC), P(z)))), "."),
    Description("The expression", SourceForm(For(z, a)), "declares", SourceForm(z), "as a locally bound variable within the scope of the arguments to this operator."))

Topics using this entry

Operators