Taylor series

noun

Tay·​lor series ˈtā-lər- 

: a power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case it has the form {latex}f(x) = f(a) + \frac{f'(a)}{1!}(x - a) + \frac{f''(a)}{2!}(x - a)^{2} + \dots + \frac{f^{[n]}(a)}{n!}(x - a)^{n}{/latex} where f[ⁿ] (a) is the derivative of nth order of f(x) evaluated at a

called also Taylor's series

Examples of Taylor series in a Sentence

Recent Examples on the Web

Intrigued by the anomaly, Martin dug into the game's source code and discovered that the landing algorithm was based on highly sophisticated physics for its time, including the Tsiolkovsky rocket equation and a Taylor series expansion. —Benj Edwards, Ars Technica, 14 June 2024

The latter is a general process known as a Taylor series expansion, which, in the case of the sine function, gives the polynomials discussed above. —Quanta Magazine, 1 June 2022

Word History

Etymology

Brook Taylor †1731 English mathematician

First Known Use

1842, in the meaning defined above