# Applied Mathematics/Fourier Series

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## Introduction[edit]

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: