I'm watching V. Balakrishnan's video lectures on Classical Physics, and right now he's going through statistical mechanics.(adsbygoogle = window.adsbygoogle || []).push({});

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 :)

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# Integral definition of factorial

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