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?
Hi, just wanted to comment on the new look. your white-on-black math expressions look kind of funny in e.g. google reader when shown against a white background.
any chance the white-on-black appearance of latex formulas could be put in the css stylesheet of your blog so that readers of the RSS feed would get the ’standard’ black-on-white appearance?
Comment by anders — January 9, 2008 @ 2:01 pm
I’m not exactly sure how I would go about that. CSS isn’t really my thing, and I’m not exactly sure how LaTeX is implemented on wordpress, so … the spirit is willing, but I sort of fail.
Comment by Fox — January 10, 2008 @ 7:19 am
You can derive that ratio limit pretty easily using Stirling’s approximation.
Comment by twistedone151 — May 11, 2008 @ 9:40 am