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

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