Taylor series

noun
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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