entire function

整函数

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

Translation evidence: Literature usage

Meaning in context

An entire function is a complex-valued function holomorphic at every finite point of C.

在整个复平面每个有限点都全纯的复值函数称为整函数，不要求在无穷远点全纯。

Example

e2ze^{2z} and z4+1z^4+1 are entire.

Usage and distinctions

Entire does not mean polynomial or bounded; an entire function that is bounded on C must be constant.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Complex Analysis§6, paragraph before Proposition 6.3 · 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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