Merriam-Webster Collegiate Dictionary - 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) + (f1(a)/1!)(x - a) + (f2(a)/2!)(x - a)? + ... + (fn(a)/n!)(x - a)? + ... where f n(a) is the derivative of nth order of f(x) evaluated at a — called also Taylor's series