History of Taylor series

Difference (from prior major revision) (minor diff)

Changed: 3c3

∑ ----- (x - a)ⁿ

∑ ------ (x - a)ⁿ

Changed: 5c5

Here, n! is the factorial of n and f ⁽ⁿ⁾(a) denotes the n-th derivative of f at the point a.

Changed: 33c33

(1+x)^α = ∑ C(α,n) xⁿ for |x| < 1 and all real α (see binomial theorem)

(1+x)^α = ∑ C(α,n) xⁿ for |x| < 1 and all complex α (see binomial theorem and binomial coefficient)

Changed: 83c83

All these expansions are also valid for complex arguments.

All these expansions are also valid for complex arguments x.

	Revision 12 . . (edit) November 27, 2001 9:51 am by AxelBoldt
	Revision 11 . . (edit) November 27, 2001 9:49 am by AxelBoldt
	Revision 10 . . (edit) November 27, 2001 9:49 am by AxelBoldt
	Revision 9 . . November 25, 2001 8:18 am by AxelBoldt [binomial theorem works for complex exponents too.]
	Revision 8 . . (edit) November 10, 2001 12:52 am by AxelBoldt [link]
	Revision 7 . . (edit) November 10, 2001 12:51 am by AxelBoldt [link]
	Revision 6 . . August 10, 2001 5:23 am by AxelBoldt [corrected all formulas]