Trigonometric series

Summary

A trigonometric series is an infinite series $\sum_{n \in \Z} c_n e^{inx}$, or $\frac{a_0}{2} + \sum_{n \ge 1} (a_n \cos nx + b_n \sin nx)$, with arbitrary coefficients. Its partial sums are trigonometric polynomials. Every Fourier series is a trigonometric series, but not every trigonometric series is the Fourier series of an integrable function. The study of these series led Cantor to set theory, through the question of uniqueness of the coefficients.