Re: laplace transform problem

From: Michael Jørgensen (ccc59035_at_vip.cybercity.dk)
Date: 03/14/05 

Date: Mon, 14 Mar 2005 07:31:23 +0100

"Bubba Smith" <Klaas.Baks@gmail-dot-com.no-spam.invalid> wrote in message
news:42352290$1_2@127.0.0.1...
> Hi, I have the following question.
>
> I am searching for a closed form solution to the following integral:
>
> Int_x=0^x=infinity exp(-px) erf( b*sqrt(x) + a/sqrt(x) ) dx
>
> where a>0, p>0 and erf(.) is the error function evaluated at .
>
> There is a book by Produnikov, Brychokov and Marichev (Integrals and
> Series Vol. 4), that lists the solution as:
>
> 1/p * exp(-2a*(sqrt(p+b^2)+b)*(b/sqrt(p+b^2)-1) + 1/p
>
> Comparing the numerical integration with the closed form solution, it
> seems that the solution is not correct. Can someone help me derive
> the correct solution?

Note that the definitions of erf() might differ by a constant factor.

-Michael.

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