## Trigonometric polynomials.

Warning:

In this subsection you need some basic knowledge on complex numbers.

We call here a trigonometric polynomial a linear combination of terms of the form , where and are non negative integers. To compute the integral of a trigonometric polynomial, we must first of all linearize it. For this purpose, we use the so-called Euler's formulae:

We will not develop the general case, but give some examples:

Example 8.2.12   Let .

We have:

. Therefore: . Check this result either by differentiation, or by using standard trigonometric identities.

Example 8.2.13   Let .

We have:

Therefore: .

Noah Dana-Picard 2007-12-28