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