formal power series

形式幂级数

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

Over a commutative ring R, a formal power series is a coefficient sequence written ∑ a_n x^n; equality is coefficientwise, addition is termwise, and multiplication uses finite convolution at each degree.

交换环 R 上的形式幂级数是写作 ∑a_n x^n 的系数列；相等与加法逐系数判定，乘法在每个次数采用有限卷积。

Example

$\sum_{n\ge0}n!x^n$ is a valid formal series over $\mathbb{Q}$.

Usage and distinctions

Formal existence does not assert convergence at any nonzero numerical argument.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Keller and Trotter — Applied Combinatorics (2016)Section 8.1, opening definition and Proposition 8.3 · Checked 2026-10-14

Translation sources

1. 上海交通大学 — CS0901 组合数学（2026）§2.1，注解2.2「形式幂级数」 · Checked 2026-10-14

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