Stirling

Op here, I ment (5) equal to (6)

>>8520001
>all in cursive
Holy crap that's annoying to read

File: stireng2.png (9KB, 435x207px) Image search: [Google]

9KB, 435x207px

>>8520004

Don't be a bitch and find an explanation

>>8520001
I'm not 100% sure, but I think (1) is just another approximation of (6) (which by itself is an approximation) for large n, as n^n grows much faster than sqrt(2*pi*n).

>>8520021
>ln in cursive

>>8520001
1-5 are not Stirling's approximation.
6 is.

Stirling's approximation is asymptotic with x!, meaning that lim x->inf x!/stirling_approx(x) = 1.
(x/e)^x does not satisfy this property.
However x/e is asymptotic to x!^(1/x).

>>8520001
why should they be equal? you just pulled both of them out of your ass with no derivation

like >>8520041 said, 1-5 are not Stirling's approximation

>>8520021
Dunno anything about what stirling even means, but sqrt(2pi*n) is definitely negligible compared to n^n

>>8520141
Oh i thought it was talking about limits for n-->inf

Ignore this comment :3