Stirling's Approximation for Large Factorials

N!\sim {\sqrt {2\pi N}}\left({\frac {N}{e}}\right)^{N}

Stirling’s approximation to the factorial asymptotically approaches the factorial as N increases. Despite the apparent complexity of the forrmula, it can be evaluated much faster than iterative computation of the factorial to full precision and is widely used in combinatorial mathematics and statistics where large factorials occur in expressions.