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MathGroup Archive 2005

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Re: "teach" mathematica an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54634] Re: "teach" mathematica an integral
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Thu, 24 Feb 2005 03:21:42 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <curp29$qvk$1@smc.vnet.net> <cv08ns$j7e$1@smc.vnet.net> <cv2dgp$2dp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cv2dgp$2dp$1 at smc.vnet.net>, "julia" <dbug at hotmail.de> 
wrote:

> Hi,
> 
> The term of a model, i need to transform is
> (0.25*a^2*Erf[(a - 2*b*x)/(2*(c*x)^0.5)])/(b^2*x^3)
> 
> (a,b,c  are parameters)
> 
> The transformation, which mathematica didn't do was
> 
> LaplaceTransform[Erf[(a - 2*b*x)/(2*Sqrt[c*x])], x, s]
> 
> I performed the transformation by partial integration. This leads to
> 
> ((-b)*E^((a*(b - a*Sqrt[c/a^2]*Sqrt[b^2/c + s]))/c) + (Sqrt[c] -
> a*Sqrt[c/a^2]*E^((a*(b - a*Sqrt[c/a^2]*Sqrt[b^2/c + s]))/c))*
> Sqrt[b^2/c + s])/(Sqrt[c]*s*Sqrt[b^2/c + s])
> 
> now i want to transform the first term. The Problem is that the
> Erf-Expression is part of a product...

The Laplace Transform of your model

 f[a_,b_,c_][x_] = a^2 Erf[(a - 2 b x)/(2 (c x)^(1/2))]/(4 b^2 x^3);

does not exist because near x = 0, Erf[(a - 2 b x)/(2 (c x)^(1/2))] -> 1 
(assuming a and c positive), so f[a,b,c][x] ~ 1/x^3. Hence
 
 Integrate[f[a,b,c][x] Exp[-x s],{x,0,Infinity}]

diverges.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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