The Taylor formula is a representation of a function as an infinite sum of terms, calculated from the values of its derivatives at a single point. This formula allows a smooth function to be approximated as a polynomial near that point. The Taylor series is typically written as:

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f^{(3)}(a)}{3!}(x-a)^3 + \cdots$

In general, for a function $f(x)$ that is infinitely differentiable at a point ( a