Re: "teach" mathematica an integral
- To: mathgroup at smc.vnet.net
- Subject: [mg54635] Re: "teach" mathematica an integral
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 24 Feb 2005 03:21:45 -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> <cv6suf$6qv$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <cv6suf$6qv$1 at smc.vnet.net>, "Scout" <user at domain.com> wrote: > > 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) One must take care in evaluating f[0]. For real parameters with a > 0 and c > 0, as x -> 0 Erf[(a - 2 b x)/(2 Sqrt[c x])] -> Erf[a/(2 Sqrt[c x])] -> 1 > 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] This is not correct. You mean Erf[Infinity], which is 1. Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul