Re: bug in Integrate (5.2)

• To: mathgroup at smc.vnet.net
• Subject: [mg74975] Re: bug in Integrate (5.2)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Fri, 13 Apr 2007 02:04:25 -0400 (EDT)
• References: <200704110557.BAA02816@smc.vnet.net><evks5v\$p1k\$1@smc.vnet.net>

```> http://forums.wolfram.com/mathgroup/archive/2006/Sep/msg00468.html

Thanks a lot for bringing in my attention this thread.

> (1) Integrate can misjudge convergence and incorrectly claim divergence.
> (2) As mentioned in the post at the above URL, if this happens, and if
> Message is blocked by Block, then Integrate can claim the result is
> infinite. This was a small (in my opinion) bug, fixed for the next releas=
e=2E

structure Block[{Message},Integrate[...]
is a (small indeed) bug.

But what I do consider as a BIG bug is that for a parameter integral
Integrate:
1) Fails completely to provide ANY regions of convergence (correct or
incorrect it
doensn't matter at this point).
2) Returns a completely wrong result of Divergence regardless the
values of the
parameters.

Of course specifying that a>0 and b>0 leads to the correct result.

Regards
Diitris

=CF/=C7 Daniel Lichtblau =DD=E3=F1=E1=F8=E5:
> dimitris wrote:
> > Consider the integral of the following function in [0,Infinity).
> >
> > In[710]:=
> > f[x_, a_, b_] := (ArcTan[x/a] - ArcTan[x/b])/x
> >
> > The integrand can be proved that converges for a, b>0.
> > [proof snipped --dl]
> >
> > However Mathematica returns
> >
> > In[725]:=
> > Block[{Message}, Integrate[f[x, a, b], {x, 0, Infinity}]]
> >
> > Out[725]=
> > Infinity
> >
> > result which came from a very bad performance of Mathematica's
> > Integrate algorithm.
>  >
> > (The ommited message is Integrate::idiv, generated when Mathematica
> > considers an integral
> > divergent.)
> > [...]
>
> This has been discussed in past.
>
> http://forums.wolfram.com/mathgroup/archive/2006/Sep/msg00468.html
>
> To recap:
>
> (1) Integrate can misjudge convergence and incorrectly claim divergence.
> (2) As mentioned in the post at the above URL, if this happens, and if
> Message is blocked by Block, then Integrate can claim the result is
> infinite. This was a small (in my opinion) bug, fixed for the next releas=
e=2E
>
> Daniel Lichtblau
> Wolfram Research

```

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