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We have: $ L^{-1}\{e^{-cs}F(s)\} = H(t - c)f(t-c) $, with $ H $ is a heaviside function.

In many documents, $ H(t - c) $ is defined as:

$ H(t - c) = \left\{\begin{matrix} 0 &, t < c \\ 1 &, t \geq c \end{matrix}\right. $

However, the Wikipedia seems to hint that the value of $ H(t - c) $ at $ t = c $ is actually of our choice. I know Wikipedia is not a reliable source but it is true that the definition of the heaviside function in the discrete form does vary at $ H(0) $.

dlmf.nist.gov defines $ H(0) $ to be $ 0 $ whereas uea.ac.uk does not define $ H(0) $.

So when we inverse the Laplace transform of a function and get the heaviside function as the result, we can define $ H(0) $ at our choice?

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