Exponential sum

In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function

${\displaystyle e(x)=\exp(2\pi ix).\,}$

Therefore, a typical exponential sum may take the form

${\displaystyle \sum _{n}e(x_{n}),}$

summed over a finite sequence of real numbers x_n.