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Re:More gaussian integration bugs
 To: mathgroup at yoda.physics.unc.edu
 Subject: Re:More gaussian integration bugs
 From: ross at macadam.mpce.mq.edu.au
 Date: Fri, 10 Apr 1992 16:21:56 +1000
This one is a doosie.
At our site the answer varies according to the version of Mathematica used:
$Version
DEC_RISC 2.0 (August 23, 1991)
Integrate[x Exp[(x1)^2] , {x, Infinity, Infinity}]
3 3
(2 E Sqrt[Pi] + HypergeometricU[, , 1])
2 2

2 E
Integrate[Exp[x^2],{x,Infinity,Infinity}]
Sqrt[Pi]
N[%2]
1.86153
N[%3]
1.77245


$Version
DEC RISC (ULTRIX) 1.2 (January 24, 1990)
Integrate[x Exp[(x1)^2] , {x, Infinity, Infinity}]
Sqrt[Pi]
Integrate[Exp[x^2],{x,Infinity,Infinity}]
Sqrt[Pi]
N[%2]
1.77245
N[%3]
1.77245


$Version
Macintosh 2.0 (December 12, 1991)
Integrate[x Exp[(x1)^2] , {x, Infinity, Infinity}]
3 3
(2 E Sqrt[Pi] + HypergeometricU[, , 1])
2 2

2 E
Integrate[Exp[x^2],{x,Infinity,Infinity}]
Sqrt[Pi]
N[%2]
1.86153
N[%3]
1.77245


The three different kernels were all tested from the same Macintosh
frontend.
Switching kernels is just a menuselection  Well done, Theo Gray and
Doug Stein!!
(The only problem is that the Integration packages on the Mac take 5
minutes to load,
using my Mac IIci, with a 5MB memory partition for Mathematica. )
The latter result above is surprising, since Paul McGuire
(pmcguire at bucknell.edu) got the
correct answer with version 2.0 on a Mac IIcx.
I have tried to use Trace on this integral, in an attempt to follow the use
of functions
from the Integrate package, but all I get is the final answer, once the
integrand has been
put into a normal form.
Setting TraceForward>True and TraceInternal>True did not help.
Would someone please shed some light on how to use Trace effectively here.
_______________________________
Ross Moore 
Mathematics Dept 
Macquarie University 
North Ryde, Sydney 
Australia 

ross at macadam.mpce.mq.edu.au 
______________________________
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