       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. 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:=
> \!\(D[Erf[\(a - 2\ b\ x\)\/\(2\ \@\(c\ x\)\)], x]\)
>
> Out=
> \!\(\(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:=
> LaplaceTransform[%1, x, s]
>
> Out=
> \!\(\(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:=
> Simplify[(%2 + Erf)/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

```

• Prev by Date: Re: Elegant syntax for multiple conditional assignment?
• Next by Date: Re: Monte Carlo Simulation Experiences
• Previous by thread: Re: "teach" mathematica an integral
• Next by thread: solve doesn't solve