Applied Mathematics/Fourier Series

For the function , Taylor expansion is possible.

This is the Taylor expansion of . On the other hand, more generally speaking, can be expanded by also Orthogonal f

Fourier series edit

For the function   which has   for its period, the series below is defined:


This series is referred to as Fourier series of  .   and   are called Fourier coefficients.


where   is natural number. Especially when the Fourier series is equal to the  , (1) is called Fourier series expansion of  . Thus Fourier series expansion is defined as follows: