
Re: Integral test
Posted:
Dec 10, 2012 6:56 PM


On Mon, 10 Dec 2012 23:51:20 GMT, aigret.not@myrealbox.invalid (Leon Aigret) wrote:
>On Mon, 10 Dec 2012 21:05:31 +0000, >=?ISO88591?Q?Jos=E9_Carlos_Santos?= <jcsantos@fc.up.pt> wrote: > >>Hi all, >> >>One of my students asked me today a question that I was unable to >>answer. Let _f_ be an analytical function from (0,+oo) into [1,+oo) and >>suppose that the integral of _f_ from 1 to +oo converges. Does it follow >>that the series sum_n f(n) converges? I don't think so, but I was unable >>to find a counterexample. Any ideas? > >If ïnto" means injectivity then the answer must obviously be yes >because _f_ is monotonous. Otherwise, f(x) = cos (pi x^2) should work >if absolute convergence of the integral is not required.
... and tried to concel it one minute later. Please ignore.
Leom

