Question

suppose that the only singularities of the function g(z) are finitely many poles which lie away from the origin and the negative real axis. show that integration of the function f(z)=g(z)lnz with -pi<arg(z)<=pi , around an appropriate keyhole contour, leads to being able to find the value of the integral g(-x)dx in terms of the residues of f(z).

Answer 1