- #1

- 532

- 31

## Homework Statement

Show that u(x, y) = y/π ∫

_{-∞}

^{∞}f(t) dt / ((x - t)

^{2}+y

^{2}) satisfies u

_{xx}+ u

_{yy}= 0.

## Homework Equations

Leibniz' Rule

## The Attempt at a Solution

I'm not even sure Leibniz' Rule can be applied here since there seems to be a discontinuity in the integrand when x=t and y=0. When I use it and take the second derivatives, I get terms that have no way of cancelling (for example the -2(x-t) and -2y terms). I also tried integration by parts first but it did not simplify things.