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August 19th, 2019, 03:36 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math  Laplace transform
How can I find the nth derivative of laplace integral ?
Last edited by idontknow; August 19th, 2019 at 03:39 AM. 
August 19th, 2019, 07:10 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 376 Thanks: 202 
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 $\displaystyle s^nF(s) + s^{n1}f(0) + s^{n2}f'(0) + s^{n2}f''(0) + … + f^{(n1)}(0)$. 

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