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."))