MathLiveStirling's approximation
Gives an asymptotic estimate of n! for large n, using a square root and an exponential term. It is used in combinatorics, statistical mechanics and asymptotic analysis when exact factorials are unwieldy.
n! \sim \sqrt{2\pi n}\left(\frac{n}{e}\right)^nWhat the symbols mean
| a positive integer (large n for the approximation to be accurate) | |
| Euler's number, the base of the natural logarithm (approximately 2.71828) | |
| the ratio of a circle's circumference to its diameter |
About this formula
- FieldMathematics
- TopicFactorials and asymptotic analysis
- LevelUniversity
- Also calledStirling's formula, factorial approximation, approximation for factorials, n factorial asymptotic, Stirling approximation for large factorials, asymptotic formula for factorial
- SourceWikidata Q470877
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