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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.

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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