How Big Are Factorials?
17 hours ago
- The post explains how to estimate the number of digits in a factorial, like 52!, using an approximation without a calculator.
- The Gamma function extends the factorial to all positive real numbers and is key to deriving Stirling's approximation.
- Stirling's approximation, derived from the Gamma function via Laplace's method, accurately estimates large factorials.
- The number of digits in n! is computed using the base-10 logarithm of Stirling's approximation, with a small constant term that adds a few digits.