# Heaviside Expansion Formula

## Theorem

Let $P, Q$ be polynomials with coefficients in $\C$.

Let $\deg Q \ge \deg P + 1$.

Let $\map Q z$ have a simple zero for $z \in X$.

Let $\map {\laptrans f} z = \dfrac {\map P z} {\map Q z}$.

Then:

$\ds \map f t = \sum_{z \mathop \in X} e^{z t} \frac {\map P z} {\map {Q'} z}$

## Source of Name

This entry was named for Oliver Heaviside.