On 3/3/12 4:01 AM, Barton Willis wrote:
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>> defint returns an incorrect "divergent" message
>> for integrals of the form
>
>> integrate ( sin(x)/x^n, x, 1, inf ) for n = even pos integer, n = 2, 4, 6, 8, 10, ...
>
> Possibly related:
>
> (%i1) assume(b>1);
> (%o1) [b>1]
>
> (%i2) integrate(sin(x)/x^2, x, 1, b);
> (%o2) gamma_incomplete(-1,%i*b)/2+gamma_incomplete(-1,-%i*b)/2-gamma_incomplete(-1,%i)/2-gamma_incomplete(-1,-%i)/2
>
> (%i3) limit(%,b,inf);
> (%o3) gamma_incomplete(-1,infinity)-gamma_incomplete(-1,%i)/2-gamma_incomplete(-1,-%i)/2
>
What version of maxima are you using? With the current git sources, I
don't get divergence for these integrals. The limit doesn't leave
infinity, but is zero, leaving just the other terms, which is also what
the infinite integral returns.
I thought Dan Gildea (?) fixed this a little while ago.
Ray