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Can anyone help me get this Laplace transform, $$ L[(f''(x))^n] $$ where $f'(0)=0$ and $f''(0)=0$ and $n$ is power of $$f''(x)$$?

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    Whether or not relevant, it is interesting to note the following (not too well-known) result: the Laplace transform of the product $f_1 (t) f_2 (t)$ is equal to the convolution of $F_1 (s)$ and $F_2 (s)$. See http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node145.html#sec:AConvolutionInFrequencyDomain2011-04-13

2 Answers 2