A formula expressing a function in terms of a polynomial approximation and an error (remainder) term. Explicitly, given a function f (x) and a real number a,
|f (x)||=||f (a) + f'(a)(x - a) + ... + f(n-1)(a) + f(n)(t)dt|
|=||pn-1(x) + rn(x)|
The approximation of a function f (x) around a point x = a by a polynomial
|pn(x) = f (a) + f'(a)(x - a) + f''(a)(x - a)2 + ... + f(n)(a)(x - a)n|
Given a function f (x), the Taylor series about x = a is
|(x - a)n|
The difference between a Taylor polynomial and a function it approximates.