Can I be Expressed in Terms of J and K for Arbitrary f,g,h?

[natski]

Hi, I have been thinking recently about integrating something with 3 parts such as:

$$I=\int_{0}^{\infty}f(x)\ast g(x)\ast h(x)\ast dx$$

If I is an unknown that we are trying to find and we know what J and K are where:

$$J=\int_{0}^{\infty}f(x)\ast g(x)\ast dx$$

and

$$K=\int_{0}^{\infty}f(x)\ast h(x)\ast dx$$

Is there enough information to find I? (Note how we cannot get rid of or change the limits).

Natski

 

[natski]

assume...

Just to add, we assume that each function is easy to differentiate or integrate by itself but the three functions multiplies is too difficult.

Natski

 

[StatusX]

If your question is, can you express I in terms of J and K for arbitrary f,g,h, the answer is no. One easy was to see this is by letting f=1. You can still integrate by parts if you use something like u=f(x)g(x), du=h(x)dx.