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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How does taylor-series compare to similar and commonly confused words? Explore the most common comparisons:

• Maclaurin series vs. Taylor series

Example Sentences

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

In this section we show how to use those Taylor series to derive Taylor series for other functions.

From Textbooks • Mar. 30, 2016

To determine if a Taylor series converges, we need to look at its sequence of partial sums.

From Textbooks • Mar. 30, 2016

We now consider the more general question: if a Taylor series for a function f converges on some interval, how can we determine if it actually converges to f ?

From Textbooks • Mar. 30, 2016

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

From Textbooks • Mar. 30, 2016