since the integrand is an even function and so the contributions from the contour in the left-half plane and the contour in the right cancel each other out. Thus, goes to zero as . See also Cauchy's integral formula Glasser's master theorem Jordan's lemma Methods of contour integration Morera's theorem Nachbin's theorem Residue at infinity Logarithmic form Notes References External links Residue theorem in MathWorld Theorems in complex analysis Analytic functions