History of Binomial coefficient

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	Revision 12 . . December 18, 2001 7:22 am by AxelBoldt [Formula about diagonals in Pascal's triangle]
	Revision 11 . . December 12, 2001 9:18 am by AxelBoldt [Why not add another random fact while we're at it :-)]
	Revision 10 . . (edit) November 28, 2001 8:36 am by (logged).112.129.xxx [added Bezier curve]
	Revision 9 . . November 28, 2001 3:46 am by AxelBoldt
	Revision 8 . . November 28, 2001 3:27 am by AxelBoldt [fun fact about prime divisors from Weisstein]
	Revision 7 . . November 28, 2001 3:04 am by AxelBoldt [link to combinations]
	Revision 6 . . November 27, 2001 9:25 am by AxelBoldt
	Revision 5 . . November 26, 2001 9:43 am by AxelBoldt
	Revision 4 . . November 26, 2001 9:41 am by AxelBoldt
	Revision 3 . . November 26, 2001 12:40 am by AxelBoldt [more formulas, proper generalization]
	Revision 2 . . November 26, 2001 12:34 am by AxelBoldt [more formulas, proper generalization]
	Revision 1 . . November 24, 2001 11:27 am by AxelBoldt [New]

Difference (from prior major revision) (author diff)

Added: 30a31

Combinatorics and statistics

Added: 39a41,42

Divisors of binomial coefficients

Added: 41a45,46

Formulas involving binomial coefficients

Added: 60a66,69

n
∑ C(n-k, k) = F(n+1) (9)
k=0
Here, F(n+1) denotes the Fibonacci numbers. This formula about the diagonals of Pascal's triangle can be proven with induction using (3).

Added: 61a71

Generalization to complex arguments

Changed: 65c75

C(z, k) = ------------------------- (9)

C(z, k) = ------------------------- (10)

Changed: 67c77

This generalization is used in the formulation of the binomial theorem and satisfies properties (3) - (8).

This generalization is used in the formulation of the binomial theorem and satisfies properties (3) and (7).