An asymptotic representation which provides approximate values of the factorials and of the gamma-function for large values of . This representation has the form
where . The asymptotic equalities
hold, and mean that when or , the ratio of the left- and right-hand sides tends to one.
The representation (*) was established by J. Stirling (1730).
See Gamma-function for the corresponding asymptotic series (Stirling series) and additional references.
|[a1]||N.G. de Bruijn, "Asymptotic methods in analysis" , Dover, reprint (1981)|
|[a2]||G. Marsaglia, J.C.W. Marsaglia, "A new derivation of Stirling's approximation of " Amer. Math. Monthly , 97 (1990) pp. 826–829|
|[a3]||V. Namias, "A simple derivation of Stirling's asymptotic series" Amer. Math. Monthly , 93 (1986) pp. 25–29|
Stirling formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stirling_formula&oldid=13618