[Tutor] factorial

[Greg Chapman]

>It gives the improbably wacky function:
>
> n!  \approx
>               \sqrt{2 \pi}  n^{n+1/2}  e^{-n}
>
>This equation is so strange that it must be true.  *grin*
>
>
>Does anyone want to code it in Python and see how it compares to the exact
>factorial function?

Maybe I got the syntax wrong on Danny's approximation version, but the way I
did it it's way off.

Can anyone tell me if I got the syntax wrong or if the function actually
doesn't work well?

import math

def apFactorial(n):                #this should be equivalent to Danny's
    return ((math.sqrt(2 * math.pi)) * (n**(n+1/2)) * (math.exp(-n)))

def reFactorial(n):                #this is Gerrit's recursive function from
his earlier post
    if n<2: return n
    else: return n*reFactorial(n-1)

def itFactorial(n):               #and here's an iterative version I threw
together
    i = n-1
    while i:
        n = n * i ; i -= 1
    return n

if __name__ == '__main__':
    print 'Approximate function:\t %d' % apFactorial(10)
    print 'Recursive function:\t %d' % reFactorial(10)
    print 'Iterative function:\t %d' % itFactorial(10)

The program output is:
Approximate function:	 1138007
Recursive function:	 3628800
Iterative function:	 3628800