Stirling's approximation Formula

Click on the image for a detailed proof

n!\approx\sqrt{2\pi n}\left(\frac{n}{e}\right)^n

Stirling’s formula is an approximation used to estimate the factorial of a large number. It provides a way to simplify this calculation for large values of n, which grow very quickly.
In Analytic number theory, it is used when studying the Gamma Function due to its connection with the factorial.
Abraham de Moivre first discovered the formula in a less precise form that was later perfected by James Stirling.

Any questions?

Feel free to contact our authors at: [email protected], you will be put directly in touch with the person who wrote the text.

Didn’t find what you were looking for?  Keep looking through all our formulas regarding the Gamma Function!

First Functional Equation
First Functional Equation
Hankel's Loop Integral
Hankel's Loop Integral
Riemann-von Mangoldt formula
Riemann-von Mangoldt formula
Definition of the Gamma Function
Definition of the Gamma Function
Euler's Infinite Product
Euler's Infinite Product
Relation to the Gamma Function 1
Relation to the Gamma Function 1

See all Formulas for the Gamma Function…

X-twitter Pinterest Threads