The Taylor series of a infinitely differentiable function \(f(x)\in\mathbb{C}\) at a single point \(a\in\mathbb{C}\) is defined as:

\({\displaystyle f(a)=\sum _{n=0}^{\infty }{\frac {f^{(n)}(a)}{n!}}(x-a)^{n}}\)

where \(f^{(n)}(a)\) denotes the \(n\)th derivative of \(f\) evaluated at the point \(a\).
- The derivative of order zero of \(f\) is defined to be \(f\) itself and \((x − a)^{0}\) and \(0!\) are both defined to be 1.