The formula to calculate Stirling's Approximation is:
\[ S(n) = \sqrt{2\pi n} \left(\frac{n}{e}\right)^n \]
Where:
Stirling's Approximation is a mathematical formula used to approximate the factorial of a large number. It is named after the Scottish mathematician James Stirling. The approximation states that the factorial of a number \(n\) is approximately equal to the square root of \(2\pi n\) times \(\left(\frac{n}{e}\right)^n\). This approximation becomes more accurate as \(n\) increases, and is particularly useful in fields such as statistics and combinatorics where factorials of large numbers are often encountered.
Let's assume the following value:
Using the formula:
\[ S(10) = \sqrt{2\pi \times 10} \left(\frac{10}{e}\right)^{10} \approx 3598695.62 \]
Stirling's Approximation for 10 is approximately 3598695.62.
