Infinite sum of sines and cosines
In mathematics, a trigonometric series is an infinite series of the form
![{\displaystyle A_{0}+\sum _{n=1}^{\infty }A_{n}\cos {nx}+B_{n}\sin {nx},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77955030eb636bbf0d5986201b743ba9e6bdf83b)
where
is the variable and
and
are coefficients. It is an infinite version of a trigonometric polynomial.
A trigonometric series is called the Fourier series of the integrable function
if the coefficients have the form:
![{\displaystyle A_{n}={\frac {1}{\pi }}\int _{0}^{2\pi }\!f(x)\cos {nx}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee7ae12764f8a83a54c08170daee3e658e53e873)
![{\displaystyle B_{n}={\frac {1}{\pi }}\displaystyle \int _{0}^{2\pi }\!f(x)\sin {nx}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d225c11ba20b96da8c9d09ac030d3da4af1ffac8)