# Fourier series

From Knowino

In mathematics, the **Fourier series**, named after Joseph Fourier (1768—1830), of a complex-valued periodic function *f* of a real variable, is an infinite series

defined by

where *T* is the period of *f*.

In what sense it may be said that this series converges to *f*(*x*) is a somewhat delicate question. However, physicists being less delicate than mathematicians in these matters, simply write

and usually do not worry too much about the conditions to be imposed on the arbitrary function *f*(*x*) of period *T* for this expansion to converge to it.

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