[[Formal calculus MOC]]
# Formal binomial expansion

Let $\mathbb{K}$ be a field with [[Characteristic|$\opn{char} \mathbb K = 0$]].
The **formal binomial expansion** is the usage of the classical [[binomial expansion]] purely formerly, defined as[^1988]
$$
\begin{align*}
(1+x)^a = \sum_{k \in \mathbb{N}_{0}} {a \choose k} x^k
\end{align*}
$$
A special case is the **formal geometric series**
$$
\begin{align*}
(1-x)^{-1} = \sum_{k \in \mathbb{N}_{0}} x^k
\end{align*}
$$

  [^1988]: 1988\. [[Sources/@frenkelVertexOperatorAlgebras1988|Vertex operator algebras and the Monster]], §3.4, p. 76

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