chaselweng wrote:

> I read a paper and see below inequality

>

> 1/sqrt(2*pi*n) * n^n * exp( -n + 1/(12*n) - 1/(360*n^3) ) <= C(n, l) <=

> 1/sqrt(2*pi*n) * n^n * exp( -n + 1/ (12*n) )

>

> where C(n,l) means the combination with n!/( l! * (n-l)! )...

> I tried to use stirling approximation, but i can't get the same

> result....

>

> Can anyone help me for any kinds of comment......
there are slightly different formulae for Stirling's approximation,

some are a little more accurate than others, but they all have the same

asymtotic behavior when n gets large. i recommend looking at

http://en.wikipedia.org/wiki/Stirling%27s_approximation
anyway it says that

n! = sqrt(2*pi*n) exp(n*log(n)-n) * exp(lambda)

where 12*n < 1/lambda < 12*n + 1

that's the best approximation and shows the error constraint. i have

also seen

n! approx= exp(n*log(n)-n)

which will also work in most cases when n is super large.

r b-j