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I Laplace transformation of nested function

  1. Nov 5, 2016 #1
    I want a formula (if there exists) to find the Laplace transformation of a nested function; a function within a function
    For example what is the LT of θ(f(t)), where θ is the step function? Is there already a formula for such things or should I follow the definition integrating etc..???
    I have searched similar tables online but I can't find anything so far..Thank you!
  2. jcsd
  3. Nov 5, 2016 #2


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    There is no hope for nested functions in general.
    For step functions we have can do it as long as we can find all the steps.
    After all a step function is just a sum of delayed constants.
    Example f=1 sin x>0 0 sin x<0
    $$\int_0^\infty \! f(t)e^{-s t}\,\mathrm{d}t=\sum_{k=0}^\infty (-1)^k \frac{1}{s} e^{-s k \pi}=\frac{1}{s(1+e^{-s \pi})}=\frac{e^{s \pi}}{s(1+e^{s \pi})}$$
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