Re: Laplace transform of [f(x)]^2

A N Niel <anniel@xxxxxxxxxxxxxxxxxxxxx> wrote in message news:<230420052026347409%anniel@xxxxxxxxxxxxxxxxxxxxx>...
> In article
> <7982674.1114287990460.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>, Roman
> Groger <groger@xxxxxxxxxxxxxx> wrote:
>
> > Hi folks.
> >
> > Does anyone have an idea how to Laplace-transform [f(x)]^2 ? It can be
> > transformed by integration by parts to a Laplace transform of f(x)*f'(x) but
> > this is equally tough. Any hint is highly appreciated.
> >
> > Thanks,
> >
> > Roman
>
> Under Laplace tranform, products become convolutions.

* * ****** * *** ***
Dear A.N Niel,

Perhaps function f(x) possesses some peculiar properties for some constant t,
I see two simple cases :f(x)= f(t-x) => convolution {f(x)*f(t-x)},
f(x)^2= m(x)*g(t-x)
Alain.
.

Relevant Pages

  • Re: Laplace transform of [f(x)]^2
    ... >> transformed by integration by parts to a Laplace transform of f*f'but ... >> this is equally tough. ... Any hint is highly appreciated. ...
    (sci.math)
  • Re: Laplace transform of [f(x)]^2
    ... > transformed by integration by parts to a Laplace transform of f*f'but ... > this is equally tough. ... Any hint is highly appreciated. ...
    (sci.math)
  • Re: Inverse Laplace transforn with not completely defined functions
    ... Hint: what's the Laplace transform of a convolution? ... Prev by Date: ...
    (sci.math)
  • Re: Infantile authours degrading this NG.
    ... > masked by his over-riding urge to be insulting and was therefore ... >over definite integrals versus antiderivatives, ... >this integration by parts is not going to work.) ... >finally get fe^for the Laplace transform. ...
    (sci.math)
  • Re: Integral of sin(x)/x
    ... better, simplest, straightest method ... ... Integration by parts, maybe? ... Assuming differentiation under the integral sign is allowed, ... then by the definition of the Laplace transform ...
    (sci.math)