Stirling Formula

The approximate value for factorial function (n!) is Stirling’s approximation. This can also be used for Gamma function. Stirling’s formula is also used in applied mathematics. It makes finding out the factorial of larger numbers easy. Lets see how we use this formula for the factorial value of larger numbers.3

The stirling formula for n numbers is given below:

\[\large n!\sim \sqrt{2\pi}\,n^{n+\frac{1}{2}}\,e^{-n}\]

 Solved example

Question: What will be the factorial of 11 using Stirling’s formula?

Solution:

Using the formula: $n!\sim \sqrt{2\pi}\,n^{n+\frac{1}{2}}\,e^{-n}$

$11!\sim \sqrt{2\pi}\,11^{11+\frac{1}{2}}\,e^{-11}$

= 99251304.16


Practise This Question

If G is the universal gravitational constant and ρ is the uniform density of a spherical planet.  Then shortest possible period of rotation around a planet can be