ATechnical Lemmas

The proof is an induction on k. Consider the general case p2k+1. It is easy to see that g (x) = ex p2k(x) and g (x) = ex p2k 1(x). By the induction hypothesis, g 0 and therefore g is convex. Thus, the minimum of g is given by its stationary points. It is easy to observe that x = 0 is indeed a stationary point. Thus, minx R g(x) = g(0) = 0, which finishes the proof.