
Mathematics 2010
A glimpse inside the mathematical kitchenDOI: 10.7153/jmi0530 Abstract: We prove the inequality sum_{k=1}^infty (1)^{k+1} r^k cos(k*phi) (k+2)^{1} < sum_{k=1}^infty(1)^{k+1} r^k (k+2)^{1} for 0 < r <= 1 and 0 < phi < pi. For the case r = 1 we give two proofs. The first one is by means of a general numerical technique (maximal slope principle) for proving inequalities between elementary functions. The second proof is fully analytical. Finally we prove a general rearrangement theorem and apply it to the remaining case 0 < r < 1. Some of these inequalities are needed for obtaining general sharp bounds for the errors committed when applying the RiemannSiegel expansion of Riemann's zeta function.
