- #1
Runei
- 193
- 17
I'm watching V. Balakrishnan's video lectures on Classical Physics, and right now he's going through statistical mechanics.
In that regards he's talking about Stirlings formula, and at one point, he wrote an integral definition of the factorial like the following
[itex]n! = \int_{0}^{\infty}dx\hspace{0.1cm}e^{-x}\hspace{0.1cm}x^n\hspace{0.1cm},\hspace{2cm} \text{where}\hspace{1cm} n={1,2,3 ...}[/itex]
Why is he writing the integral in that way? With the dx first and the exponentials afterwards?
I thought the definition was
[itex]n! = \int_{0}^{\infty}e^{-x}x^ndx[/itex]
Can anybody explain this?
Many thanks in advance :)
In that regards he's talking about Stirlings formula, and at one point, he wrote an integral definition of the factorial like the following
[itex]n! = \int_{0}^{\infty}dx\hspace{0.1cm}e^{-x}\hspace{0.1cm}x^n\hspace{0.1cm},\hspace{2cm} \text{where}\hspace{1cm} n={1,2,3 ...}[/itex]
Why is he writing the integral in that way? With the dx first and the exponentials afterwards?
I thought the definition was
[itex]n! = \int_{0}^{\infty}e^{-x}x^ndx[/itex]
Can anybody explain this?
Many thanks in advance :)