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

*To*: mathgroup at smc.vnet.net*Subject*: [mg64127] Re: [mg64100] does anybody know how to find the inverse Laplace transform of this wierd thing?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 2 Feb 2006 00:05:37 -0500 (EST)*References*: <200602010934.EAA23043@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

gino wrote: > 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! > We start with your input. In[9]:= InputForm[hH[s_] = 1/s^2*Exp[s^2*a^2/2]*Integrate[Exp[-u^2/2], {u,s*a,Infinity}, Assumptions->Element[a,Reals]]] Out[9]//InputForm= (E^((a^2*s^2)/2)*Sqrt[Pi/2]*Erfc[(a*s)/Sqrt[2]])/s^2 Then the inverse Laplace transform is computed as below. In[11]:= InputForm[InverseLaplaceTransform[hH[s], s, t, Assumptions->Element[a,Reals]]] Out[11]//InputForm= Sqrt[Pi/2]*(a*(-1 + E^(-t^2/(2*a^2)))*Sqrt[2/Pi] + t*Erf[t/(Sqrt[2]*a)]) You will need to decide for yourself whether this is what you had in mind. Daniel Lichtblau Wolfram Research

**References**:**does anybody know how to find the inverse Laplace transform of this wierd thing?***From:*"gino" <loseminds@hotmail.com>