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I Laplace transforms of y^n

  1. Mar 5, 2016 #1
    Let's say you have a function y(t). You know how derivatives of y have their own Laplace transforms? Well I was wondering if powers of y such as y^2 or y^3 have their own unique Laplace transforms as well. If so , how do you calculate them (because plugging them into the usual integral doesn't seem to work)?
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  3. Mar 6, 2016 #2


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  4. Mar 6, 2016 #3


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    Are you sure? I don't see such a formula. Unless you are mistaking the one for ##f^{(n)}(t)## which is the n'th derivative. I have never seen a formula for ##\mathcal L f(t)^n## and I don't think there is a general one.
    Last edited: Mar 6, 2016
  5. Mar 7, 2016 #4


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    Yes sorry I confuse the notation, I fact there isn't and explicit formula for this ...
  6. Apr 21, 2016 #5
    On that same wikipedia page, there seems to be a way to do that if we consider the Laplace transform of the multiplication of functions; we just take the function [itex] f(t) [/itex] and multiply it [itex] n [/itex] times.
  7. Apr 24, 2016 #6
    Laplace transform is an efficient tool when linear operations are involves (sum, derivative, integral).
    But it is not so, and generaly very complicated, when non-linear operations are involved (multiplication, division, power). Even in the simplest cases convolution is requiered, which is generaly arduous.
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