The Sinc function \mathrm{sinc}(x) = \frac{\sin(x)}{x} can be represented by a series for example:

\mathrm{sinc}(x) = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \frac{x^6}{7!} + \cdots

This series can be derived by a Taylor expansion.

A Fourier series can be used to represent the Sinc function but only over a specific interval for x.