= Singular integral equation
{title2=$a(t)f(t)+b(t)\operatorname{PV}\int_\Gamma K(t,\zeta)f(\zeta)d\zeta=c(t)$}
An integral equation with a kernel singular on the integration <contour> needs a prescribed limiting interpretation such as a <Cauchy principal value>. For the Cauchy kernel, the <Sokhotski–Plemelj theorem> converts a linear scalar equation into a <Riemann-Hilbert problem> for its two analytic boundary values. Normalization, endpoint regularity and the index of that jump determine homogeneous freedom and solvability.
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