TAYLOR'S SERIES

[Tay.lor's series] n [Brook Taylor d. 1731 Eng. mathematician] (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 the first term of the series is f(a) and the (n + 1)st term consists of the factor (x - a) raised to the exponent n and multiplied by a coefficient consisting of a fraction whose numerator is the derivative of nth order of f(x) evaluated at a and whose denominator is n! --called also Taylor series