A Fourier series is a mathematical technique that breaks down periodic functions into an infinite series of sinusoidal harmonics.

The trigonometric Fourier series represents a periodic function with a specific period using sine and cosine functions. The frequency of these functions is inversely proportional to the period of the original function.

The constant terms and the individual contribution of each sine and cosine function to the original function are understood using Fourier coefficients. The calculation of these coefficients involves integration over one period.

For a Fourier series to depict a periodic function, the Dirichlet conditions must be satisfied.

The first condition demands that the function have a finite integral over one period.

The second condition states that the function's variation should be limited within any given range.

Lastly, the function must have a finite number of discontinuities within any specific range, none of which can be infinite.

Fourier series can be used to approximate functions - it cannot fully recover functions that do not meet Dirichlet's conditions.