- #1
Arian.D
- 101
- 0
[tex] \int_0^\infty e^{-x^2}dx \int_0^\infty e^{-y^2}dy = \int_0^\infty \int_0^\infty e^{-(x^2+y^2)} dxdy[/tex]
Under what conditions we could do the same for other functions? I don't get how Poisson (or Euler, or Gauss, whoever that did this for the first time) realized that this is true. It looks quite ingenious to me and I wonder if there's a theorem or something that I could apply to similar cases and this case as well.
Under what conditions we could do the same for other functions? I don't get how Poisson (or Euler, or Gauss, whoever that did this for the first time) realized that this is true. It looks quite ingenious to me and I wonder if there's a theorem or something that I could apply to similar cases and this case as well.