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

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

Later in this section, we will show examples of finding Taylor series and discuss conditions under which the Taylor series for a function will converge to that function.

From Textbooks • Mar. 30, 2016

The Taylor series for ex, sin x, and cos x converge to the respective functions for all real x.

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

Taylor series for functions can often be derived by algebraic operations with a known Taylor series or by differentiating or integrating a known Taylor series.

From Textbooks • Mar. 30, 2016