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MathGroup Archive 2005

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Re: "teach" mathematica an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54316] Re: "teach" mathematica an integral
  • From: "julia" <dbug at hotmail.de>
  • Date: Thu, 17 Feb 2005 10:30:38 -0500 (EST)
  • Organization: Fraunhofer Gesellschaft (http://www.fraunhofer.de/)
  • References: <curp29$qvk$1@smc.vnet.net> <cv08ns$j7e$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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...





"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> schrieb im Newsbeitrag
news:cv08ns$j7e$1 at smc.vnet.net...

> Hi,
>
> define:
>
> g /: Integrate[g[x_], x_] := q[x]
>
> and
>
> Integrate[g[z], z]
>
> gives
>
> q[z]
>
> since you hav not given the correct form fo the function you wish
>
> to integrate, I can only advice to use the most general form of te
> integration, i.e.,
>
> instead of the definition above
>
> Unprotect[Integrate]
> Integrate[a_.*g[x_] + c_., x_] /; FreeQ[a, x] := a q[x] + c
> Protect[Integrate]
>
> Regards
>
>   Jens
>
>
>
> "julia" <dbug at hotmail.de> schrieb im Newsbeitrag
> news:curp29$qvk$1 at smc.vnet.net...
> > Hi group,
> >
> > I've had an integral (a laplace-transformation) which mathematica
doesn't
> > know.
> > Now i have an analytic expression for the integral.
> > Is there a possibility to add the new integral to mathematica (for
example
> > in any kind of library)?
> > My problem is, that this integral is only a part of a longer formula for
> > which i need the transformation...
> >
> > Thanks!
> >
> >
>
>



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