1. Show, by contour integration, that if a > 0 and ξ ∈ R then and check that 2....

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.]

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