Re: does anybody know how to find the inverse Laplace transform of this wierd thing?

*To*: mathgroup at smc.vnet.net*Subject*: [mg64114] Re: does anybody know how to find the inverse Laplace transform of this wierd thing?*From*: "Scout" <Scout at nodomain.com>*Date*: Thu, 2 Feb 2006 00:04:59 -0500 (EST)*References*: <drq0ij$ms6$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"gino" <loseminds at hotmail.com> > Want to find the inverse Laplace transform of the following term: > > H(s)=1/s^2*exp(s^2*a^2/2)*integrate(exp(-u^2/2), u from s*a to +infinity) > > How to do that? > > ------------------------------ > > Making relaxation to the problem, if I have to find only certain sampled > values of the inverse Laplace transform of H(s), let's denote it as h(t), > > I just need to find h(1), h(2), h(3), etc. > > Is there a short cut for it? > > Thanks a lot! > > Gino, I've given your H[s_]:= ... function to Math5.2 running on WinXP and I've obtained this result in few seconds with InverseLaplaceTransform[H[s],s,t] : \!\(\@\(\[Pi]\/2\)\ \((a\ \((\(-1\) + \[ExponentialE]\^\(-\(t\^2\/\(2\ a\^2\)\ \)\))\)\ \@\(2\/\[Pi]\) + t\ Erf[t\/\(\@2\ a\)])\)\) (paste it in your Mathematica front-end) Assuming 'a' as a constant and t is the new variable. Bye, ~Scout~