Let denote the zeta function. Prove that
Let be analytic in the disk . Prove that:
It follows from Taylor that and the convergence is uniform. Hence,
We have that and for we also have that due to
So if then lies within the disk ; hence the integral equals whereas if then lies outside the disk ; hence
Find all functions that preserve convergent serieses.
Let be positive real numbers such that . Prove that
Due to the AM – GM we have that