0
$\begingroup$

$$ \int_0^L{dx_1 \int_0^{x_1}{dx_2 \cdots \int_0^{x_{n-1}}{dx_n f(|x_i-x_j|)} } } =\frac{1}{n!} \int_0^L{dx_1 \int_0^{L}{dx_2 \cdots \int_0^{L}{dx_n f(|x_i-x_j|)} } } $$ where $f(|x_i-x_j|)$ means a function dependent on all possible $|x_i-x_j|\,,i\ne j$.

What is the condition of $f$ that satisfies this identity? Thanks.

$\endgroup$
  • $\begingroup$ Are you sure it is not $L^n/n!$ instead of $1/n!$ ? $\endgroup$ – Tom-Tom Dec 14 '17 at 14:35
  • $\begingroup$ @Tom-Tom Sure.. $\endgroup$ – xiaohuamao Dec 14 '17 at 14:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.