What is "trigonometric series"

n. (context mathematics English) Any series of the form $frac\{1\}\{2\}A\_\{o\}+displaystylesum\_\{n=1\}^\{infty\}(A\_\{n\}\; cos\{nx\}\; +\; B\_\{n\}\; sin\{nx\}).$

A trigonometric series is a series of the form:

$\frac{A_{0}}{2}+\displaystyle\sum_{n=1}^{\infty}(A_{n} \cos{nx} + B_{n} \sin{nx}).$

It is called a Fourier series if the terms A and B have the form:

$$A_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \cos{nx} \,dx\qquad (n=0,1,2,3 \dots)$$

$$B_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \sin{nx}\, dx\qquad (n=1,2,3, \dots)$$

where f is an integrable function.