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The factorial function: Stirling’s formula

Published online by Cambridge University Press:  01 August 2016

David Fowler
David Fowler*
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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Extract

How big is n!? For example, to pluck a number out of thin air, what is the order of magnitude of 272! ?

This is the third note of a series on the factorial. The two previous notes [1] and [2] dealt with the factorial function x! while here we only consider n! when n is an integer, but its main results also apply to non-integer arguments. This note is longer and more elaborate than the previous ones, but the principal result is in the opening section. Only aficionados need go any further.

Type
Articles
Information
The Mathematical Gazette , Volume 84 , Issue 499 , March 2000 , pp. 42 - 50
Copyright
Copyright © The Mathematical Association 2000

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References

1. Fowler, D. H. A simple approach to the factorial function, Math. Gaz. 80 (1996) pp. 378–381.Google Scholar
2. Fowler, D. H. The factorial function: the next steps, Math. Gaz. 83 (1999) pp. 53–58.CrossRefGoogle Scholar
3. Robbins, H. A remark on Stirling’s formula, American Mathematical Monthly 62 (1955) pp. 26–29.Google Scholar
4. Stirling, D. S. G. Mathematical analysis, a fundamental and straightforward approach, Ellis Harwood & John Wiley, Chichester, Brisbane, & Toronto (1987).Google Scholar
5. Tweddle, I. James Stirling: ‘This about series and such things’, Scottish Academic Press, Edinburgh (1988).Google Scholar