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IEVref: | 103-04-07 | ID: | |

Language: | en | Status: Standard | |

Term: | inverse Laplace transform | ||

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Definition: | representation of a real or complex function f(t) of the real variable t by the integral transformation $f(t)=\frac{1}{2\pi \text{j}}{\int}_{\text{\hspace{0.05em}}\sigma -\text{j}\infty}^{\text{\hspace{0.05em}}\sigma +\text{j}\infty}F(s){\text{e}}^{s\text{\hspace{0.05em}}t}\text{d}s$ where $F(s)$ is the Laplace transform of the function | ||

Publication date: | 2009-12 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO | ||

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$f(t)=\frac{1}{2\pi \text{j}}{\int}_{\text{\hspace{0.05em}}\sigma -\text{j}\infty}^{\text{\hspace{0.05em}}\sigma +\text{j}\infty}F(s){\text{e}}^{s\text{\hspace{0.05em}}t}\text{d}s$

where $F(s)$ is the Laplace transform of the function *f*(*t*), *σ* is greater or equal to the abscissa of convergence of $F(s)$ and j is the imaginary unit