Concept

# Dirichlet–Jordan test

Summary
In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of the values of the discontinuity). It is one of many conditions for the convergence of Fourier series. The original test was established by Peter Gustav Lejeune Dirichlet in 1829, for piecewise monotone functions. It was extended in the late 19th century by Camille Jordan to functions of bounded variation (any function of bounded variation is the difference of two increasing functions). Dirichlet–Jordan test for Fourier series The Dirichlet–Jordan test states that if a periodic function f(x) is of bounded variation on a period, then the Fourier series S_n(f(x)) converges, as n\to\infty, at each point of the domain to \lim_{
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Related people

Related units