Stirling's Formula is a mathematical formula that approximates the factorial of a large number n. It is expressed as n! ≈ √2πn (n/e)^n.
Stirling's Formula was first derived by Scottish mathematician James Stirling in the 18th century. He used the method of asymptotic expansions to approximate the factorial function when n is large.
Stirling's Formula is significant because it provides a quick and accurate approximation of factorials for large numbers, which can be difficult to calculate directly. It has many applications in fields such as statistics, physics, and computer science.
Stirling's Formula is only accurate for large values of n. As n gets smaller, the approximation becomes less accurate. It also does not work well for negative values of n.
No, Stirling's Formula is only valid for positive integers. It cannot be used to approximate the factorial of non-integer numbers.