If we define the 'factorial function' as...
... with a little of patience we 'discover' that is...
... where is the 'Euler's constant'. To be continued in a succesive post...
The solution I had in mine is totally different.
Using the fact that (Integrate both sides of the Maclaurin series for and don't forget about the constant ).
The integrand is always positive, so you don't have to worry about something potentially going haywire when you switch the order of integration.