Prev: Different results with ReplaceAll and direct substitution
Next: proper supremum norm implementation
From: Leslaw Bieniasz on 7 Apr 2010 07:26

Hi,

I need to find an inverse Laplace transform of the
expression:

Sqrt[s*(s+a)]/(s-b)

where "s" is the Laplace variable, "a" is a real positive constant,
and "b" is a real constant that can be either positive or negative.
I have tried the InverseLaplaceTransform[] function, but it
returns the original expression. My question is: does this mean
that the inverse transform does not exist, or only Mathematica
cannot find it?
Also, if anybody knows where I could possibly find the inverse
in any book, or how I might obtain the inverse otherwise, I would
appreciate an information. Abramowitz and Stegun book does not have it.

Leslaw

From: Leslaw Bieniasz on 8 Apr 2010 08:02


Hi,

I have reformulated my problem, and now I am getting different terms
in the form:

1/Sqrt[s*(s+a)]/(s-b)

for which the inverse Laplace transform should exist.
However, MATHEMATICA still does not give me the formula for
the inverse. It returns the correct inverse for 1/Sqrt[s*(s+a)],
but not for the above expression, to which it should, in principle,
apply the convolution theorem.

Leslaw



On Wed, 7 Apr 2010, Leslaw Bieniasz wrote:

>
> Hi,
>
> I need to find an inverse Laplace transform of the
> expression:
>
> Sqrt[s*(s+a)]/(s-b)
>
> where "s" is the Laplace variable, "a" is a real positive constant,
> and "b" is a real constant that can be either positive or negative.
> I have tried the InverseLaplaceTransform[] function, but it
> returns the original expression. My question is: does this mean
> that the inverse transform does not exist, or only Mathematica
> cannot find it?
> Also, if anybody knows where I could possibly find the inverse
> in any book, or how I might obtain the inverse otherwise, I would
> appreciate an information. Abramowitz and Stegun book does not have it.
>
> Leslaw
>
>

*-----------------------------------------------------------------------*
| Dr. Leslaw Bieniasz, |
| Institute of Physical Chemistry of the Polish Academy of Sciences, |
| Department of Complex Systems and Chemical Processing of Information |
| ul. Niezapominajek 8, 30-239 Cracow, Poland. |
| tel. (room) +48 (12) 6395212 tel./fax. (secretariat) +48 (12) 4251923 |
| E-mail: nbbienia(a)cyf-kr.edu.pl |
| and |
| Faculty of Physics, Mathematics and Applied Computer Science, |
| Cracow University of Technology, |
| ul. Warszawska 24, 31-155 Cracow, Poland. |
*-----------------------------------------------------------------------*
| Interested in Computational Electrochemistry? |
| Visit my web site: http://www.cyf-kr.edu.pl/~nbbienia |
*-----------------------------------------------------------------------*

From: dh on 8 Apr 2010 08:04
On 07.04.2010 13:26, Leslaw Bieniasz wrote:
> Hi,
>
> I need to find an inverse Laplace transform of the
> expression:
>
> Sqrt[s*(s+a)]/(s-b)
>
> where "s" is the Laplace variable, "a" is a real positive constant,
> and "b" is a real constant that can be either positive or negative.
> I have tried the InverseLaplaceTransform[] function, but it
> returns the original expression. My question is: does this mean
> that the inverse transform does not exist, or only Mathematica
> cannot find it?
> Also, if anybody knows where I could possibly find the inverse
> in any book, or how I might obtain the inverse otherwise, I would
> appreciate an information. Abramowitz and Stegun book does not have it.
>
> Leslaw
>

Hi Leslaw,
a conditions for the existence of the inverse Laplace transform of F[s] is:
Limit[F[s],s->Infinity] == 0
this is not the case for your expression.
cheers, Daniel


--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh(a)metrohm.com>
Internet:<http://www.metrohm.com>


 | 
Pages: 1
Prev: Different results with ReplaceAll and direct substitution
Next: proper supremum norm implementation