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MathGroup Archive 2007

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Re: bug in Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74810] Re: bug in Integrate
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Fri, 6 Apr 2007 04:19:41 -0400 (EDT)
  • References: <ev2b70$kh1$1@smc.vnet.net>

Aha!

The key is the setting GenerateConditions->True.

But even though I have encountered one a couple of integrals that
the explicit setting GenerateConditions->True was necessary for getting
desirable results, it still looks mysterious why it is needed to add this
setting since the default options of Integrate contain it!

Ooops...

Options[Integrate]
{Assumptions :> $Assumptions, GenerateConditions -> Automatic,
PrincipalValue -> False}

I have forgotten this!

Consequently, the default setting is GenerateConditions -> Automatic
and so for this integrals
Integrate[...,GenerateConditions -> Automatic] (*default*)
fail to detect the divergence.

Information[GenerateConditions]
"GenerateConditions is an option for Integrate that specifies whether
explicit conditions on parameters should be generated in \
the results of definite integrals."
Attributes[GenerateConditions] = {Protected}

BUT

Reading from the help-browser...

"The default setting is GenerateConditions->Automatic, which is
equivalent to a setting of True for one dimensional integrals".

Now I get more confused!

Can you give a little more insight?

Thanks again!
Dimitris

=CF/=C7 Bhuvanesh =DD=E3=F1=E1=F8=E5:
> Thanks for the report. This has already been fixed in the development ver=
sion for quite a while. In this case, you can get the expected divergence u=
sing GenerateConditions->True, which does more extensive checking:
>
> In[1]:= $Version
>
> Out[1]= 5.2 for Microsoft Windows (June 10, 2005)
>
> In[2]:= Integrate[x*BesselJ[0, x]*Cos[x], {x, 0, Infinity}, GenerateCon=
ditions->True]
>
> Integrate::idiv: Integral of x BesselJ[0, x] Cos[x] does not converge on =
{0, Infinity}.
>
> Out[2]= Integrate[x BesselJ[0, x] Cos[x], {x, 0, Infinity}, GenerateCon=
ditions -> True]
>
> In[3]:= Integrate[x*BesselJ[0, x]*Sin[x], {x, 0, Infinity}, GenerateCon=
ditions->True]
>
> Integrate::gener: Unable to check convergence.
>
> Integrate::idiv: Integral of x BesselJ[0, x] Sin[x] does not converge on =
{0, Infinity}.
>
> Out[3]= Integrate[x BesselJ[0, x] Sin[x], {x, 0, Infinity}, GenerateCon=
ditions -> True]
>
> Bhuvanesh,
> Wolfram Research.



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