History of Factorial

	Revision 17 . . August 9, 2001 10:43 pm by AxelBoldt [correct gamma function]
	Revision 16 . . August 9, 2001 10:04 pm by FallenAngel

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Difference (from prior major revision) (no other diffs)

Changed: 9c9

There is also the related gamma function, which can be defined for all non-negative real numbers (and even for all complex numbers for a suitable cut?) in such a way that gamma(x+1) = x! when x is a positive integer. By using this relation, we can define x! for all non-negative real numbers.

A good approximate formula for factorials is n! ~ (2 π n)1/2 (n/e)n, which is known as Stirling's Formula, after [James Stirling]?, the mathematician who discovered it. It is quite accurate when n is large, however it has to be interpreted right: it means that the quotient of the two functions approaches 1 as n approaches infinity; it does not mean that their difference approaches zero.

Changed: 11,12c11,14

A good approximate formula for factorials is n! ~ (2 π n)1/2 (n/e)n, which is known as Stirling's Formula, after [James Stirling]?, the mathematician who discovered it. It is quite accurate when n is large, however it has to be interpreted right: it means that the quotient of the two functions approaches 1 as n approaches infinity; it does not mean that their difference approaches zero.

The related gamma function Γ(z) can be defined for all complex numbers z except for z = 0, -1, -2, -3, ... It has the property :Γ(n+1) = n! when n is a positive integer. By using this relation, we can extend the definition of factorials and define z! for all complex numbers z except the negative integers.