Re: Wolfram Research QA process defect: Bug in Mathematica 6 - Integrate - 62 (Sqrt, BesselJ, MULTIPLE regression bug, false convergence)

On 30 , 10:58, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
Our little demo continues... Hello again from the VM machine
which is still ignored by CAS manufacturers.

This example demonstrates YET ANOTHER case of bad defects in
Wolfram Research Quality Assurance process.

First, in 1996, Mathematica 3.0 returns a message about the
divergence of the integral. Then, in 2002, in Mathematica 4.2
the functionality is broken. Then, in 2005, in Mathematica 5.2,
it is repaired.

Now, in Mathematica 6, this functionality is broken AGAIN!

----------------------------------------------------------------

N[Integrate[Sqrt[1 + z^2] BesselJ[1, z]^2, {z, 0, Infinity}]]

----------------------------------------------------------------
VERSION OUTPUT RESOLUTION
----------------------------------------------------------------

Mathematica 6.0 0.21953 <-------------------------------- BUG

Mathematica 5.2 Integral does not converge

Mathematica 4.2 0.21953 <-------------------------------- BUG

Mathematica 3.0 Integral does not converge

----------------------------------------------------------------

Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing

Hi Vladimir.

Try the option GenerateConditions->True.

In Mma 5.2 many times it tries harder in convergence/divergence
issues. May be this holds in version 6.

In[4]:=
(Integrate[Sqrt[1 + z^2]*BesselJ[1, z]^2, {z, 0, Infinity},
GenerateConditions -> #1] & )
/@ {False, True, Automatic}

\!\(\*
RowBox[{\(Integrate::"idiv
"\), \(\(:\)\(\ \)\), "\"\<Integral of Sqrt[
1 + z^2]*BesselJ[1, z]^2 does not converge on {0,Infinity}. \!\(
\*ButtonBox[\(More...\),
ButtonData:>\\\"Integrate::idiv\\\",
ButtonStyle->\\\"RefGuideLinkText\\\",
ButtonFrame->\\\"None\\\"]\)\>\""}]\)

\!\(\*
RowBox[{\(Integrate::"idiv
"\), \(\(:\)\(\ \)\), "\"\<Integral ofSqrt[1 +
z^2]*BesselJ[1, z]^2 does not converge on {0,Infinity}. \!\(
\*ButtonBox[\(More...\),
ButtonData:>\\\"Integrate::idiv\\\",
ButtonStyle->\\\"RefGuideLinkText\\\",
ButtonFrame->\\\"None\\\"]\)\>\""}]\)

Out[4]=
{MeijerG[{{1/2, 1/2}, {}}, {{0, 1}, {-1, -1}}, 1]/(4*Pi),
Integrate[Sqrt[1 + z^2]*BesselJ[1, z]^2, {z, 0, Infinity},
GenerateConditions -> True], Integrate[Sqrt[1 + z^2]*BesselJ[1,
z]^2, {z, 0, Infinity}, GenerateConditions -> Automatic]}

Dimitris

.