It becomes of interest, in a number of areas, to be able to approximate, for a given value of n, the value of
This is a difficult expression, as are most all expressions involving factorial, so it is convenient to have a good approximation.
Playing around with logs and integrals, I was able to derive the following approximation, that
Indeed, for large n, the two functions are practically proportional to each other. And, most interestingly of all, according to Mathematica, calculating out that limit,
Neat, no?
