Fourier series

Summary

The Fourier series of a periodic function writes it as a sum of sines and cosines, or of complex exponentials $e^{inx}$. Its coefficients are computed by integrals. It turns problems about periodic functions into problems about sequences of coefficients. Whether and in which sense the series converges back to the function is a central question of harmonic analysis. Parseval's identity and Fejér's theorem give two answers.