If you evaluate the complex function f(x)=z^n on the unit circle z=exp(it), you obtain cos(nt)+i sin(nt). Thus Fourier series are "just" Taylor series evaluate

If you evaluate the complex function f(x)=z^n on the unit circle z=exp(it), you obtain cos(nt)+i sin(nt). Thus Fourier series are "just" Taylor series evaluated on the unit circle.