I am trying to learn about Fourier analysis. And the following question came up: While I know that the main motivation behind Fourier analysis, is to be able to represent a periodic function as a series that consists out of cosine and sine functions. I don't really understand why we do not just use normal polynomials i.e. just use the Taylor series.
I am assuming that the reason, is that, when using a Taylor series, some problems arise. But I can't figure out where the problem would be. I would be very thankful if someone could show me an example or explain where the problem is.