=+13. Suppose the continuous function f(t) on [0, ∞) is O(ect) for some c ≥ 0 as t → ∞. For t positive use Laplace’s method to prove Post’s inversion formula [161]

f(t) = limk→∞

(−1)k k!

k t

k+1 ˜f(k)

k t

for the Laplace transform ˜f(s) of f(t). Here ˜f(k)

(s) is the kth derivative of the transform. (Hint: Consult Section 12.3.1.)