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:

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

Proof

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Source of Name

This entry was named for Oliver Heaviside.

Sources

• 1999: Jerrold E. Marsden and Michael J. Hoffman: Basic Complex Analysis (3rd ed.): $8.2.3$: Heaviside Expansion Formula