# Taylor series

Tay·​lor series | \ ˈtā-lər- \

## 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

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## The first known use of Taylor series was in 1842

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Cite this Entry

“Taylor series.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Taylor%20series. Accessed 18 Jan. 2022.

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