Taylor series

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) ( x 0 ) ( x−x 0 ) n/n !, where f (n) ( x 0 ) is the derivative of order n evaluated at point x 0 .

Word History and Origins

Origin of Taylor series¹

1905–10; after Brook Taylor

Example Sentences

With the CA’s “retrieval process” under way, we glimpse one of the series’ international stars: Iain Glen, star of the Jack Taylor series, Downton Abbey and Game of Thrones.

From The Guardian

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

From BusinessWeek

The Taylor series of a function is the limit of that function’s Taylor polynomials, provided that the limit exists.—,

From BusinessWeek

"In fact he was partly responsible for its creation after telling Tim Taylor, series producer, that it would be possible to evaluate a site in only three days," a biography on the Time Team website says.

From BBC

"In fact he was partly responsible for its creation after telling Tim Taylor, series producer, that it would be possible to evaluate a site in only three days," it says.

From BBC