Fungrim entry: 2be0b5

Symbol: MeromorphicLimit —

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

— Limiting value, allowing poles

This operator is equivalent to ComplexLimit except that whereas ComplexLimit in general is undefined when

a

is a pole (because the direction of the resulting infinity depends on the direction of approach), MeromorphicLimit is taken to give UnsignedInfinity (

{\tilde \infty}

) when

a

is a pole.

Definitions:

Fungrim symbol	Notation	Short description
`MeromorphicLimit`	$\lim_{z \to a} f(z)$	Limiting value, allowing poles
`ComplexLimit`	$\lim_{z \to a} f(z)$	Limiting value, complex variable
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity

Source code for this entry:

Entry(ID("2be0b5"),
    SymbolDefinition(MeromorphicLimit, MeromorphicLimit(f(z), For(z, a)), "Limiting value, allowing poles"),
    Description("This operator is equivalent to", SourceForm(ComplexLimit), "except that whereas", SourceForm(ComplexLimit), "in general is undefined when", a, "is a pole (because the direction of the resulting infinity depends on the direction of approach),", SourceForm(MeromorphicLimit), "is taken to give", SourceForm(UnsignedInfinity), "(", UnsignedInfinity, ")", "when", a, "is a pole."))

Topics using this entry

Operators