I've understood Taylor series as being the representation of a "transcendental" function, using power functions with coefficents represented by appropriate derivatives. (Or maybe it is the MacLauren series, where $\cos x= 1-\frac{x^2}{2!}+\frac{x^4}{4!}+…$)
I've understood Fourier series as being the representation of periodic linear functions using integral coefficients multiplied by transcendental functions.
Is my understanding correct in either or both cases? And if one consists of derivatives and the other of integrals, does that mean that Fourier series are the converse (or "inverse") of Taylor series?
Best Answer
Just a brief comparison:
Fourier series are:
On the other hand:
Taylor series are: