exponential generating function

指数生成函数

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

Other names / variants: EGF

Translation evidence: Literature usage

Meaning in context

For a sequence (a_n) in a commutative algebra over the rational numbers, its exponential generating function is the formal series ∑ a_n x^n/n!.

有理数上的交换代数中，数列 (a_n) 的指数生成函数是形式级数 ∑a_n x^n/n!。

Example

The counts an=4na_n=4^n give EGF e4xe^{4x}.

Usage and distinctions

The count is n![x^n]A(x), not merely the coefficient of x^n; division by factorials needs an appropriate coefficient algebra.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 8.6, opening definition · Checked 2026-10-14

Translation sources

  1. 上海交通大学 — CS0901 组合数学（2026）§2.4，定义2.13「指数生成函数」 · Checked 2026-10-14
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