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Fungrim entry: 2be0b5

Symbol: MeromorphicLimit limzaf(z)\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 aa 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 aa is a pole.
Definitions:
Fungrim symbol Notation Short description
MeromorphicLimitlimzaf(z)\lim_{z \to a} f(z) Limiting value, allowing poles
ComplexLimitlimzaf(z)\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."))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC