Taylor series

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

Definition of Taylor series

: 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

First Known Use of Taylor series

1842, in the meaning defined above

History and Etymology for Taylor series

Brook Taylor †1731 English mathematician

Keep scrolling for more

Learn More about Taylor series

Time Traveler for Taylor series

Time Traveler

The first known use of Taylor series was in 1842

See more words from the same year

Statistics for Taylor series

Cite this Entry

“Taylor series.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Taylor%20series. Accessed 5 Dec. 2020.

Comments on Taylor series

What made you want to look up Taylor series? Please tell us where you read or heard it (including the quote, if possible).


Test Your Vocabulary

Musical Words Quiz

  • gramophone
  • Which word describes a musical performance marked by the absence of instrumental accompaniment?
Spell It

Can you spell these 10 commonly misspelled words?


Test Your Knowledge - and learn some interesting things along the way.

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!