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