ABSTRACT
The inverse of a Laplace transform f ¯ ( s ) $ \bar{f}(s) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108858/f4dff3a2-1feb-457b-a709-022257f02721/content/inline-math20_1.tif"/> can be expressed in terms of the inversion integral: f ( t ) = L - 1 { f ¯ ( s ) } = 1 2 π i lim β → ∞ ∫ γ - i β γ + i β e st f ¯ ( s ) d s . $$ f(t) = {\mathcal{L}}^{{ - 1}} \{ \bar{f}(s)\} = \frac{1}{{2\pi i}}\mathop {\lim }\limits_{{\beta \to \infty }} \mathop \smallint \limits_{{\gamma - i\beta }}^{{\gamma + i\beta }} e^{{st}} \bar{f}(s)ds. $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108858/f4dff3a2-1feb-457b-a709-022257f02721/content/math20_1.tif"/>
