Deriving the integral of exp((x₁² + x₂² + ... + xₐ²)^(r/2))

  • Topic:
  • Thread starter Thread starter Another1
  • Start date Start date
  • Tags Tags
    Integral
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 1K views
Another1
Messages
39
Reaction score
0
stat1.png


Question
\[ \int dx_1dx_2...dx_d e^{(x^2_1+x^2_2+...+x^2_d)^{r/2}} = \frac{\pi ^{d/2}(d/r)!}{(d/2)!} \]

How can I derive this answer?
 
Physics news on Phys.org