From: Fred Nastos <4ffn@qlink.queensu.ca>
Subject: Re: Maple Integration. Buggy?!?!?
Date: 27 Jul 2000 20:32:59 GMT
Newsgroups: sci.math.symbolic,comp.soft-sys.math.maple
Summary: [missing]

In sci.math.symbolic sahai@my-deja.com wrote:
: I was surprised to find that Maple apparently has
: a bug in its symbolic integration code. I found it
: in both Maple V5.1 and 6.0 on both Sun and Linux

While we're on the topic of buggy... load up Maple (the following
happens on either 5.1 or 6) and immediately try this

> int(BesselJ(1,a*x)*BesselJ(1,b*x)/x,x=0..infinity);

Maple gives me 1/2 b/a. It shouldn't be evaluating this since
it doesn't know that b<a. The answer can be found in Watson's
Treatise of Bessel Functions (if I remember correctly). Now if
we restart Maple and supply some assumptions:

> assume(a>0):                                       
> assume(b>0):                                       
> additionally(a>b):                                 
> int(BesselJ(1,a*x)*BesselJ(1,b*x)/x,x=0..infinity);

The result is
                  infinity
                 /
                |          BesselJ(1, a~ x) BesselJ(1, b~ x)
                |          --------------------------------- dx
                |                          x
               /
                 0

when it should (ideally) be now be giving 1/2 b/a. It does seem
to kind of know the answer (when the assumptions are not made).
There a few examples like this that I've come across when dealing
with Bessel functions.