1. Show, by contour integration, that if a > 0 and ξ ∈ R then
and check that
2. Suppose Q is a polynomial of degree ≥ 2 with distinct roots, none lying on the real axis. Calculate
in terms of the roots of Q. What happens when several roots coincide?
[Hint: Consider separately the cases ξ < 0, ξ = 0, and ξ > 0. Use residues.]