For what it's worth, commercial macsyma seems to fail on
these problems
with
Proviso: Assuming p>0
OTHER-J-CASES-TO-FOLLOW.
....
RJF
Raymond Toy wrote:
> Has anyone ever looked at the tests in rtest14 for specint? It looks
> like the tests true results are whatever maxima produced and no one
> really checked the results against other sources.
>
> I'm pretty sure specint( t^(1/2)*%h[3/4,2](t)*%e^(-p*t),t) is wrong.
> (%h[3/4,2](t) is Hankel function of the second type.)
>
> And clearly
>
> specint(t^(1/2)*%ibes[1](t)*%e^(-p*t),t);
> sqrt(%pi)*%ibes[1](t)/(2*p^(3/2)) $
>
> isn't really what we wanted to test. (Partially my fault for not
> changing %ibes[1](t) to bessel_i(1,t), but I don't think I changed the
> expected result at all.)
>
> Also specint(t^(1/2)*bessel_j[3/4,2](t)*%e^(-p*t),t) is wrong
> because it gets the wrong branch cut or something, at least when
> compared to the result in Tables of Integral Transforms. Our result
> appears to have an extra factor of (-1)^(3/8) compared to that table.
>
> Ray
>
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