# I Laplace transforms of y^n

1. Mar 5, 2016

### space-time

Let's say you have a function y(t). You know how derivatives of y have their own Laplace transforms? Well I was wondering if powers of y such as y^2 or y^3 have their own unique Laplace transforms as well. If so , how do you calculate them (because plugging them into the usual integral doesn't seem to work)?

2. Mar 6, 2016

3. Mar 6, 2016

### LCKurtz

Are you sure? I don't see such a formula. Unless you are mistaking the one for $f^{(n)}(t)$ which is the n'th derivative. I have never seen a formula for $\mathcal L f(t)^n$ and I don't think there is a general one.

Last edited: Mar 6, 2016
4. Mar 7, 2016

### Ssnow

Yes sorry I confuse the notation, I fact there isn't and explicit formula for this ...

5. Apr 21, 2016

### UnivMathProdigy

On that same wikipedia page, there seems to be a way to do that if we consider the Laplace transform of the multiplication of functions; we just take the function $f(t)$ and multiply it $n$ times.

6. Apr 24, 2016

### JJacquelin

Laplace transform is an efficient tool when linear operations are involves (sum, derivative, integral).
But it is not so, and generaly very complicated, when non-linear operations are involved (multiplication, division, power). Even in the simplest cases convolution is requiered, which is generaly arduous.