1. ## laplace function

I want to calculate the Laplace transformation L{e^-[(λt)^2]t}(s).????

Thanks
Katerina
xx

2. Originally Posted by paola
I want to calculate the Laplace of L{e^-[(λt)^2]t}(s).????

Thanks
Katerina
xx
Your notation is hard to understand

I'm not sure if you mean L { te^-[(λt)^2] } or L { e^(-[(λt)^2]t) }

or L{e^-[(λt)^2]t} = L{t e^-(2λt)}

And it is called the Laplacer transform.

And why is there an (s) ?

I know that

F(s) = L { f(t) }

3. good note."Laplace transform"

f(s)=L{ f(s)=L{te-((λt)^2)}
does this make sense ????
Katerina
xx

4. Originally Posted by paola
good note."Laplace transform"

f(s)=L{ f(s)=L{te-((λt)^2)}
does this make sense ????
Katerina
xx
$\displaystyle LT[t f(t)] = -F'(s)$ where $\displaystyle F(s) = LT[f(t)]$.

Since $\displaystyle f(t) = e^{-(\lambda t)^2}$ you should read this: Laplace Transform Of A Gaussian Function