Formal calculus MOC

Formal binomial expansion

Let 𝕂 be a field with [[Characteristic|char⁡𝕂 =0]]. The formal binomial expansion is the usage of the classical binomial expansion purely formerly, defined as¹

(1+𝑥)𝑎=∑𝑘∈ℕ0(𝑎𝑘)𝑥𝑘

A special case is the formal geometric series

(1−𝑥)−1=∑𝑘∈ℕ0𝑥𝑘

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Footnotes

1. 1988. Vertex operator algebras and the Monster, §3.4, p. 76 ↩