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MathGroup Archive 1992

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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[-(x-1)^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[-(x-1)^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[-(x-1)^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
front-end.
Switching kernels is just a menu-selection --- 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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