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.
Compare Maclaurin series.
Origin of Taylor series
1905–10; after Brook Taylor
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019