Taylor series

American  

noun

Mathematics.

1. 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 x 0 , 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 x 0 .

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Etymology

Origin of Taylor series

1905–10; after Brook Taylor

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• Maclaurin series vs. Taylor series

Example Sentences

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Taylor series

The applications of Taylor series in this section are intended to highlight their importance.

From Textbooks ● Mar. 30, 2016

Therefore, if a function f has a power series at a, then it must be the Taylor series for f at a.

From Textbooks ● Mar. 30, 2016

If a function f has a power series representation at x = a, then it is given by its Taylor series at x = a.

From Textbooks ● Mar. 30, 2016

This theorem allows us to bound the error when using a Taylor polynomial to approximate a function value, and will be important in proving that a Taylor series for f converges to f .

From Textbooks ● Mar. 30, 2016

Not only is this theorem useful in proving that a Taylor series converges to its related function, but it will also allow us to quantify how well the nth Taylor polynomial approximates the function.

From Textbooks ● Mar. 30, 2016