= Finite-endpoint branch-cut jump integral
{title2=$F(-x-i0)-F(-x+i0)$}
A pair of oppositely directed <contours> on a <branch cut> produces the difference of the two boundary values integrated over their actual endpoint interval. Replacing finite endpoints by zero and infinity requires a limiting argument and convergence of the combined <improper integral>. Individual side integrals may diverge even when their difference converges, so cancellation must precede separation of endpoint limits.
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