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 functions or Trigonometric functions.
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: