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MathGroup Archive 2005

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Re: "teach" mathematica an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54490] Re: "teach" mathematica an integral
  • From: "julia" <dbug at hotmail.de>
  • Date: Tue, 22 Feb 2005 04:22:50 -0500 (EST)
  • Organization: Fraunhofer Gesellschaft (http://www.fraunhofer.de/)
  • References: <curp29$qvk$1@smc.vnet.net> <cv08ns$j7e$1@smc.vnet.net> <cv2dgp$2dp$1@smc.vnet.net> <cv6suf$6qv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

That's not the problem...
I already did the transformation like you proposed now.
But this expression is only a part of a very long model.
for example, how can i transform
(c*Erf[(a - 2*b*t)/(2*Sqrt[c]*Sqrt[t])])/(2*b^2*t^2)

with the known transformation of the Erf-Term....?


"Scout" <user at domain.com> schrieb im Newsbeitrag
news:cv6suf$6qv$1 at smc.vnet.net...
> > LaplaceTransform[Erf[(a - 2*b*x)/(2*Sqrt[c*x])], x, s]
>
> Have you tried with this Laplace property?
>
> L[f '(t)] = s * L[f(t)] - f(0)
>
> In[1]:=
> \!\(D[Erf[\(a - 2\ b\ x\)\/\(2\ \@\(c\ x\)\)], x]\)
>
> Out[1]=
> \!\(\(2\ \[ExponentialE]\^\(-\(\((a - 2\ b\ x)\)\^2\/\(4\ c\ x\)\)\)\ \
> \((\(-\(b\/\@\(c\ x\)\)\) - \(c\ \((a - 2\ b\ x)\)\)\/\(4\ \((c\ \
> x)\)\^\(3/2\)\))\)\)\/\@\[Pi]\)
>
> In[2]:=
> LaplaceTransform[%1, x, s]
>
> Out[2]=
> \!\(\(2\ \((\(-\(\(a\ \[ExponentialE]\^\(\(a\ b\)\/c - \@\(a\^2\/c\)\ \
> \@\(b\^2\/c + s\)\)\ \@\[Pi]\)\/\(2\ \@\(a\^2\/c\)\ \@c\)\)\) - \(b\ \
> \[ExponentialE]\^\(\(a\ b\)\/c - \@\(a\^2\/c\)\ \@\(b\^2\/c + s\)\)\ \
> \@\[Pi]\)\/\(2\ \@c\ \@\(b\^2\/c + s\)\))\)\)\/\@\[Pi]\)
>
> In[3]:=
> Simplify[(%2 + Erf[0])/s]
>
> Out[3]=
> \!\(\(-\(\(\[ExponentialE]\^\(\(a\ b\)\/c - \@\(a\^2\/c\)\ \@\(b\^2\/c + \
> s\)\)\ \((b\ \@\(a\^2\/c\) +
>               a\ \@\(b\^2\/c + s\))\)\)\/\(\@\(a\^2\/c\)\ \@c\ s\
> \@\(b\^2\/c \
> + s\)\)\)\)\)
>
> Does It help you?
>
> ~Scout~
>
> "julia" <dbug at hotmail.de> ha scritto nel messaggio
> news:cv2dgp$2dp$1 at smc.vnet.net...
> > 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...
> >
> >
> >
>



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