power series in analysis

幂级数

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

Translation evidence: Literature usage

Meaning in context

A power series centered at a is a series sum_{n>=0} c_n(z-a)^n with real or complex coefficients, studied as a function on the points where its partial sums converge.

分析中的幂级数由以同一中心为基点的非负整数次幂组成，在部分和收敛的点集上定义一个函数。

Example

$\sum_{n=0}^\infty (x/3)^n=1/(1-x/3)$ for $|x|<3$.

Usage and distinctions

An analytic power series has a convergence domain; a formal power series in algebra is defined without numerical convergence.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Michael Taylor — Introduction to Analysis in One Variable§3.3, equations (3.3.1)–(3.3.5) and Proposition 3.3.1 · Checked 2026-10-14

Translation sources

1. 北京大学数学科学学院 — 数学分析（实验班）课程介绍第三部分，级数理论：三、幂级数 · Checked 2026-10-14

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