Question about the maclaurin serie and laplace transform

[Lorens]

Question about the maclaurin serie and the laplace transform.

For maclaurin serie i wonder, the function used for the maclaurin development must be derivativable to infinity?

What is the difference between the fouri transform and the laplace transform? As i understood it, it's just the same except that the la place transform can converge for more functions.

 

[HallsofIvy]

Yes, to form the MacLaurin series, or more generally Taylor series, of a function the function must be infinitely differentiable. Of course, that doesn't guarantee that the series will converge, or that, it it does converge, it will converge to the value of the function!

In a certain sense (a very complicated sense!) the Fourier series is a complex version of the Laplace series.