= Riemann-Hilbert problem
{c}
{title2=$F_+-F_-=J$}
Find functions analytic on the two sides of a contour whose boundary values obey a prescribed jump, with suitable normalization at infinity and other distinguished points. An additive jump $J$ on a counterclockwise closed contour is solved by the <Cauchy integral formula> $F(k)=(2\pi i)^{-1}\int J(\zeta)/(\zeta-k)d\zeta$, subject to the normalization and compatibility conditions. The <Sokhotski–Plemelj theorem> verifies the jump.
Back to article page
