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