Taylor series

Taylor series
an approximation of a given function f at a particular point x, in terms of values of the function and its derivatives at a neighboring point x0, by a power series in which the terms are given by f(n)(x0) (x-x0)n/n!, where f(n)(x0) is the derivative of order n evaluated at point x0. Cf. Maclaurin series.
[1905-10; after BROOK TAYLOR]

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      in mathematics, expression of a function f—for which the derivatives (derivative) of all orders exist—at a point a in the domain of f in the form of the power series

∑  ∞n = 0  f (n) (a) (z − a)n/n!
in which Σ denotes the addition of each element in the series as n ranges from zero (0) to infinity (∞), f (n) denotes the nth derivative of f, and n! is the standard factorial function. The series is named for the English mathematician Brook Taylor (Taylor, Brook). If a = 0 the series is called a Maclaurin series, after the Scottish mathematician Colin Maclaurin (Maclaurin, Colin).

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Universalium. 2010.

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