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