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Inverse Laplace transform

In mathematics, the inverse Laplace transform of a functionF{\displaystyle F} is a real function f{\displaystyle f} that is piecewise-continuous, exponentially-restricted (that is, |f(t)|≤Meαt{\displaystyle |f(t)|\leq Me^{\alpha t}}∀t≥0{\displaystyle \forall t\geq 0} for some constants M>0{\displaystyle M>0} and ⁠α∈R{\displaystyle \alpha \in \mathbb {R} }⁠) and has the property: L{f}(s)=F(s),{\displaystyle {\mathcal {L}}\{f\}(s)=F(s),}where L{\displaystyle {\mathcal {L}}} denotes the Laplace transform.

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