meromorphic function

亚纯函数

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A meromorphic function on a complex domain is holomorphic except at a discrete set of poles, with the identically infinite function excluded here.

复区域上的函数若除去离散的极点集后全纯，则称为亚纯函数；此处约定不包括恒取无穷的函数。

Example

1/(z2−4)1/(z^2-4) is meromorphic on C and has poles at 22 and −2-2.

Usage and distinctions

Poles are allowed, but essential singularities and interior accumulation of poles are not.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Complex Analysis§11, meromorphic definition after Proposition 11.3, printed p.127 · Checked 2026-10-14

Translation sources

  1. 肇庆学院 —《复变函数》课程教学大纲第五章，学习要求8：整函数与亚纯函数，printed p.9 · Checked 2026-10-14
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