Date: Feb 11, 2013 1:15 AM
Author: quasi
Subject: Re: Is this series uniformly convergent for x != 0 ?

quasi wrote:>vv <vanamali@netzero.net> wrote:>>>>I'd be grateful if someone can throw light on whether or not >>the following series is uniformly convergent for x not equal >>to zero:>>>>\sum_{n=1}^infty exp(-ixn)/n>>I could be wrong, but here's what I think ...>>If k is a nonzero integer then for x = 2*k*Pi, the series >diverges. >>More generally, I think the series diverges for x = (2*k*Pi)/d >where k,d are nonzero integers with d odd and with k,d >relatively prime. Thus, the series is pointwise divergent on a >dense subset of R, so the question of uniform convergence is >silly.>>In fact, going out on a limb, it seems to me that the series>diverges for all real numbers x except for x = 0, x = Pi, >x = -Pi.I meant: except for x = Pi, x = -Pi.quasi