4 ms·
Can someone explain to me how Int[0,∞](t^{n+1} x^n e^{-tx} dx) = Int[0,∞](x^n e^{-x} dx)? That is, the last two equations of section 1.
by goerz 6y ago
Can someone explain to me how Int[0,∞](t^{n+1} x^n e^{-tx} dx) = Int[0,∞](x^n e^{-x} dx)? That is, the last two equations of section 1.
- anon_tor_12345 6y agoLet t -> 1 which you can do because this entire trick is about interchanging limits (since both an integral and a derivative are limits)
- goerz 6y agoAh, thanks! So it's just "has to hold for all values of t > 0, including for t = 1"