[[Formal calculus MOC]]
# Formal exponential

Let $\mathbb{K}$ be a field with [[Characteristic|$\opn{char} \mathbb K = 0$]].
The **formal exponential** refers to purely formal usage of the [[exponential function]] as a power series, i.e. $\exp z \in \mathbb{K}\D[z\D] \leq \mathbb{K} \{ z \}$ is defined by #m/def/fcalc 
$$
\begin{align*}
\exp z = \sum_{n \in \mathbb{N}_{0}} \frac{z^n}{n!}
\end{align*}
$$


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