defint "divergent" message incorrect



-----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

Tracing limit and ?limit while evaluating integrate(sin(x)/x^2, x, 1, b) shows that the limit bug shown in (%o3)
might be partially to blame for  integrate(sin(x)/x^2, x, 1, inf) --> divergent. 

--bw