A simple proof of Stirling's formula for the gamma function

where and the notation means that as . C = 2π f (n) ∼ g(n) f (n) / g(n) → 1 n → ∞ A great deal has been written about Stirling's formula. At this point I will just mention David Fowler's Gazette article [1], which contains an interesting historical survey. The continuous extension of factorials is, of course, the gamma function. The established notation, for better or worse, is such that equals rather than . Stirling's formula duly extends to the gamma function, in the form Γ (n) (n − 1)! n!