1
$\begingroup$

Let be $K(x,y)=\frac{2x_n}{n\alpha(n)}\frac{1}{\vert x-y\vert^n}$ where n is the dimension and $\alpha(n)$ is the volume o unitary sphere in $R^n$, $x=(x_1,...,x_n)\in R^n$ and $y=(y_1,...,y_{n-1},0)\in\partial R^n_+$. Show that:

$\int_{\partial R^n_+}K(x,y)dy=1$

Thanks in advance!

  • 0
    Right. I found: $I=\frac{2x_n(n-2)\alpha(n-2)}{n\alpha(n)}\lim_{\rightarrow\infty}\int_0^R\frac{r^{n-2}}{(r^2+x_n^2)^\frac{n}{2}}dr$. It looks like strange.2012-11-02

0 Answers 0