Taylor series


Tay·​lor series ˈtā-lər- How to pronounce Taylor series (audio)
: 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

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'Taylor series.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History


Brook Taylor †1731 English mathematician

First Known Use

1842, in the meaning defined above

Time Traveler
The first known use of Taylor series was in 1842

Dictionary Entries Near Taylor series

Cite this Entry

“Taylor series.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Taylor%20series. Accessed 2 Oct. 2023.

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