On Tue, Dec 12, 2006 at 03:33:30PM +0000, miguel lopez wrote:
> Daniel Lakeland <dlakelan <at> street-artists.org> writes:
>
> >
> > On Tue, Dec 12, 2006 at 02:09:27PM +0000, miguel lopez wrote:
> >
> > > I think that there is a long life for mathematician,
> >just not to be replaced by a computer program :).
> > >
> > > Best wishes to the list.
> >
> > Indeed. I think it should be possible to prove that:
> if
> > integral(f(x),x,0,inf) diverges then
> integral(periodic_function(x) * f(x)) should also diverge.
>
> but I haven't tried yet.
> >
> > In any case, I'll file this as a bug ...
> >
> You can not prove it: it is false:
>
>
> f(x) = 1/x diverge, f(x) * sin(x) = sin(x)/x converge.
> (30 seconds time in ultramaxima code, to discover this :)
Whoops. :-) That was exactly the first example I posted...
But I guess what I meant was if f(x) is not absolutely integrable on
[0,inf) then periodic_function(x) * f(x) should not be absolutely
integrable. (this is where my initial questions for maxima were coming
from)
The idea being that although oscillations around 0 may cause an
integral to converge, absolute integrability is dependant on the speed
at which f(x), the nonperiodic function, goes to zero at infinity. A
periodic function won't affect that rate.
It's intuitive but not rigorous, perhaps you have a counterexample in
your pocket :-)
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan