Re: A simple integral
- To: mathgroup at smc.vnet.net
- Subject: [mg47606] Re: [mg47596] A simple integral
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 18 Apr 2004 04:15:03 -0400 (EDT)
- References: <200404170631.CAA16293@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 17 Apr 2004, at 15:31, Dr A.H. Harker wrote:
> 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
>
>
The price of progress ;-)
However, note that (in 5.0)
Integrate[x^2*Exp[-(x - $B&L(B)^2/(2*$B&R(B^2)], {x, -Infinity, Infinity},
Assumptions -> {$B&R(B > 0}]
Sqrt[2*Pi]*$B&R(B*($B&L(B^2 + $B&R(B^2)
Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/
- References:
- A simple integral
- From: "Dr A.H. Harker" <a.harker@ucl.ac.uk>
- A simple integral