Laplace transforms be converted to fourier transforms?

[monty37]

can equations involving laplace transforms be converted to Fourier transforms?

 

[quantumdude]

Fourier transforms are special cases of Laplace transforms. In the Laplace transform you typically start with a function f(t) and transform it to a function F(s), where s is a complex variable. For definiteness: s=\sigma + i\omega, \sigma ,\omega\in\mathbb{R}. Let \mathcal{F} denote Fourier transformation and let \mathcal{L} denote Laplace transformation.

Then:

\mathcal{F}[f(t)]=\mathcal{L}[f(t)]|_{\sigma =0}

 

[monty37]

are Fourier transforms defined for tan functions as they are defined for sine and cosine
functions?and where do we use these transforms?