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
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