Taylor series
noun Etymology: Brook Taylor died 1731 English mathematician Date: 1842 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 f(x) = f(a) + (f[1](a)/1!)(x - a) + (f[2](a)/2!)(x - a)² + ... + (f[n](a)/n!)(x - a)ⁿ + ... where f [n](a) is the derivative of nth order of f(x) evaluated at a — called also Taylor's series

New Collegiate Dictionary. 2001.

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