# 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.

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Compare Maclaurin series.

## Origin of Taylor series^{}

1905–10; after Brook Taylor

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018