Contour deformation
= Contour deformation
A contour deformation changes the path of a <contour integral> through a region where its integrand is a <holomorphic function>. The <Cauchy integral theorem> preserves the integral when the endpoints are fixed and the connecting boundary terms vanish. Crossing a <pole> instead contributes the appropriately oriented <residue>; a <branch cut> limits which deformations are permitted on one analytic sheet.