Trigonometric polynomial

Summary

A trigonometric polynomial is a finite linear combination of the functions $e^{inx}$, $n \in \Z$, or equivalently of $1$, $\cos nx$ and $\sin nx$. Trigonometric polynomials are the partial sums of Fourier series. They are dense in the continuous $2\pi$-periodic functions, so they play for periodic functions the role that ordinary polynomials play on a closed interval.