Meromorphic continuation
= Meromorphic continuation
A <meromorphic continuation> extends a <holomorphic function> from a connected open <set> to a larger connected domain as a <meromorphic function>, allowing isolated poles. Equality on the initial open <set> determines the extension uniquely by the <identity theorem>. <Integral> formulas whose integrands depend holomorphically on a parameter often supply such an extension after contour deformation or subtraction of singular terms.