Taylor’s_formula

Definition

Let

$$ f\left. (x) \right. = a_{0} + a_{1} + a_{2}x^{2} + a_{3}x^{3} + a_{4}x^{4} + a_{5}x^{5} + \cdots $$

be defined on some non-trivial centered at zero. Then,

$$ a_{n} = \frac{f^{\left. (n) \right.\left. (0) \right.}}{n!} $$