= Dirichlet's theorem on Fourier series
{c}
{title2=$S_Nf(x)\to[f(x-)+f(x+)]/2$}
= Dirichlet convergence theorem for Fourier series
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{synonym}
One standard sufficient form states that the <Fourier series> of a piecewise continuously differentiable periodic <function> converges at $x$ to $[f(x-)+f(x+)]/2$. At a continuity point it equals $f(x)$. This modern sufficient form should be distinguished from the exact hypotheses of the 1829 original.<Sur la convergence des séries trigonométriques by Peter Gustav Lejeune Dirichlet>{ref}
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