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IEVref: | 103-04-05 | ID: | |

Language: | en | Status: Standard | |

Term: | Laplace transform | ||

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Definition: | for a real or complex function f(t) of the real variable t, complex function F(s) of a complex variable s, given by the integral transformation $F(s)={\displaystyle {\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}+\infty}f(t){\mathrm{e}}^{-s\text{\hspace{0.05em}}t}\mathrm{d}t}$ Note 1 to entry: If Note 2 to entry: 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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$F(s)={\displaystyle {\int}_{\text{\hspace{0.05em}}0}^{\text{\hspace{0.05em}}+\infty}f(t){\mathrm{e}}^{-s\text{\hspace{0.05em}}t}\mathrm{d}t}$

Note 1 to entry: If *t* is time, the variable *s* represents complex angular frequency.

Note 2 to entry: The Laplace transform of the function *f* is also denoted L*f* or ℒ*f*.