[nimish]

expand an analytic function in its taylor series then find its values on the unit circle. There's a Fourier series.

But the Fourier series uses global data than the taylor series which uses point data so they aren't perfect analogs.

A laplace transform is a fourier transform rotated in the complex plane (more or less), and if you allow the transform to take complex "frequencies" then they are basically unified. The difference is that the laplace transform is all about causal functions of time (t<0 => f(t) = 0) where as the fourier transform is less picky.