A function, $f(x)$ may be written as a [Fourier series](Fourier%20series.md) if it meets the following three conditions: ^224e47 1. It is [absolutely integrable](Absolutely%20integrable%20functions.md) ([$\int_Idx\,|f(x)|<\infty$](Absolutely%20integrable%20functions#^64e889) within a specified interval $I.$) ^b3048a 2. There must be a finite number of local extrema of $f$ in the same interval, $I,$ for which the function is [absolutely integrable.](Dirichlet%20conditions#^b3048a) ^01e60c 3. $f(x)$ muset have a finite number of [discontinuities](Discontinuities) in the interval $I$ ^5dd055 %%The conditions as they're given here are from page 282 of Altland and von Delft.%% #MathematicalFoundations/Analysis/FourierAnalysis #MathematicalFoundations/Analysis/FourierAnalysis/Integrals