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 .

---

Etymology

Origin of Taylor series

1905–10; after Brook Taylor

Compare meaning

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

• Maclaurin series vs. Taylor series

Example Sentences

See Examples For:

Taylor series

In this example, we differentiated a known Taylor series to construct a Taylor series for another function.

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

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

In general, Taylor series are useful because they allow us to represent known functions using polynomials, thus providing us a tool for approximating function values and estimating complicated integrals.

From Textbooks ● Mar. 30, 2016

Next, we show how to find power series representations for many more functions by introducing Taylor series.

From Textbooks ● Mar. 30, 2016