removable complex singularity

可去奇点

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

Translation evidence: Literature usage

Meaning in context

An isolated singularity a of a holomorphic f is removable if a value can be assigned at a so that f extends holomorphically to the whole disk.

去心圆盘上的全纯函数若能在中心补一个值，使其在整圆盘全纯，则中心为可去奇点。

Example

(ez−1)/z=1+z/2+z2/6+⋯(e^z-1)/z=1+z/2+z^2/6+\cdots extends with value 11 at 00.

Usage and distinctions

A removable real discontinuity needs a continuous extension; here the extension must be holomorphic.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Complex Analysis§11, removable-singularity definition and Theorem 11.1, printed p.126 · Checked 2026-10-14

Translation sources

  1. 肇庆学院 —《复变函数》课程教学大纲第五章，第二节 解析函数的孤立奇点，可去奇点，printed p.9 · Checked 2026-10-14
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