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... > > > > > > >