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A simple integral

• To: mathgroup at smc.vnet.net
• Subject: [mg47596] A simple integral
• From: "Dr A.H. Harker" <a.harker at ucl.ac.uk>
• Date: Sat, 17 Apr 2004 02:31:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

A simple integration, under Version 4.1.2:

Integrate[x^2 Exp[-(x-$B&L(B)^2/(2 $B&R(B^2)],{x,-$B!g(B,$B!g(B}]

       2
If[Re[$B&R(B ] > 0, 
 
                   2
  Sqrt[2 Pi] Sqrt[$B&R(B ] 
 
     2    2
   ($B&L(B  + $B&R(B ), 
 
                    2
                   x
  Integrate[----------------, 
                    2     2
             (x - $B&L(B) /(2 $B&R(B )
            E
 
   {x, -Infinity, Infinity}]]

and the same under 5.0

Integrate[x^2 Exp[-(x-$B&L(B)^2/(2 $B&R(B^2)],{x,-$B!g(B,$B!g(B}]

       2            $B&L(B
If[Re[$B&R(B ] > 0 && Re[--] < 0, 
                     2
                    $B&R(B
 
                   2    2
    Sqrt[2 Pi] $B&L(B ($B&L(B  + $B&R(B )
  -(----------------------), 
                 2
                $B&L(B
           Sqrt[--]
                 2
                $B&R(B
 
                    2
                   x
  Integrate[----------------, 
                    2     2
             (x - $B&L(B) /(2 $B&R(B )
            E
 
   {x, -Infinity, Infinity}, 
 
   Assumptions -> 
 
       $B&L(B               2
    Re[--] >= 0 || Re[$B&R(B ] <= 0
        2
       $B&R(B
 
    ]]

Two questions:
    1. Whence the extra condition in Version 5?
    2. Why the negative sign in Version 5? Using PowerExpand then gives
a negative result for this integral which is patently, for real
parameters, positive.

Am I alone in feeling that Version 5 has introduced more problems than
it has solved?

 Dr A.H. Harker
 Department of Physics and Astronomy
 University College London
 Gower Street
 LONDON
 WC1E  6BT
 (44)(0)207 679 3404
 a.harker at ucl.ac.uk

• Follow-Ups:
  • Re: A simple integral
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>