
Re: Integral test
Posted:
Dec 11, 2012 12:44 PM


On Monday, December 10, 2012 10:45:40 PM UTC8, José Carlos Santos wrote: > On 10/12/2012 23:15, Butch Malahide wrote: > > > > >> 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. > > > > > > Do you mean from [1,+oo) into (0,+oo)? > > > > Yes! My mistake. :( > > > > Best regards, > > > > Jose Carlos Santos
The function f(x) = sum_{n=1..infinity} exp(n^3*(xn)^2) has sum_n f(n) divergent but int_{x=0..inf} f(x) dx convergent. It has continuous derivatives of all orders at any x, but I don't know if it is analytic.
RGV

