COD#M-1** Taylor and Maclaurin series

The Taylor series of a real or complex valued function $f(x)$ that is infinitely differentiable functionat a real or complex number $a$ is the power series

\begin{equation}
f(x) = f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots.

\end{equation}

if $a=0$ then Taylor series becomes Maclaurin series of $f(x)$

\begin{equation}
f(x) = f(0)+\frac {f'(0)}{1!} x+ \frac{f''(0)}{2!} x^2+\frac{f^{(3)}(0)}{3!}x^3+ \cdots.
\end{equation}