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August 19th, 2019, 03:36 AM   #1
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Laplace transform

How can I find the n-th derivative of laplace integral ?

Last edited by idontknow; August 19th, 2019 at 03:39 AM.
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August 19th, 2019, 07:10 PM   #2
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Do you mean the Laplace transform of $\displaystyle \frac{d^nf}{dt^2}$?
If $\displaystyle f(t)\mapsto F(s)$, then $\displaystyle f^{(n)}(t) \mapsto s^nF(s)$ if $\displaystyle f(t)=0 ~\forall~ t<0$ (such as a step, ramp, etc.). In the general case, it maps to $\displaystyle s^nF(s) + s^{n-1}f(0) + s^{n-2}f'(0) + s^{n-2}f''(0) + … + f^{(n-1)}(0)$.
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