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MathGroup Archive 1992

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More gaussian integration bugs

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: More gaussian integration bugs
  • From: pmcguire at amethyst.bucknell.edu
  • Date: Wed, 8 Apr 92 09:56:22 EDT

 lsf at holmes.astro.nwu.edu (Sam Finn) noted that the following incorrect
computation
 occurred with Mathematica on a Sparcstation:
Mathematica version 2.0.4.5

The following integral is incorrect. The sign of the result is a clear
tip-off; moreover, it is a tabulated integral and can be found in
Gradshteyn & Ryzhik (3.462 4).


Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
 -- OPEN LOOK graphics initialized -- 

In[1]:= Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}]

                                         3  3
        -(2 E Sqrt[Pi] + HypergeometricU[-, -, 1])
                                         2  2
Out[1]= ------------------------------------------
                           2 E

In[2]:= N[%]

Out[2]= -1.86153

The difficulty seems to be machine dependent as I got the correct result
using Mathematica 2.0 on a MacIIcx with no problem.  To recognize this as
the correct answer it is easy to see the integral is the same as
 Integrate[Exp[-x^2]],{x,-Infinity,Infinity].

Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}]
Pi^(1/2)
N[%]
1.772453850905516027

Paul McGuire
pmcguire at bucknell.edu






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