Definition:Trigonometric Series

Definition
A trigonometric series is a series of the type:


 * $\map S x = \dfrac {a_0} 2 + \displaystyle \sum_{n \mathop = 1}^\infty \paren {a_n \cos n x + b_n \sin n x}$

where:
 * the domain of $x$ is the set of real numbers $\R$
 * the coefficients $a_0, a_1, a_2, \ldots, a_n, \ldots; b_1, b_2, \ldots, b_n, \ldots$ are real numbers independent of $x$.

The coefficient $a_0$ has the factor $\dfrac 1 2$ applied for convenience of algebraic manipulation.

Also known as
Some sources give this as trigonometrical series. prefers to standardise on the shorter version.