The Maclaurin series expansion of $\mathrm{f}(x)$ is a series of ascending powers of $x$ of the form
\[
\mathrm{f}(x) = \sum_{n=0}^{\infty} c_n x^n = c_0 + c_1 x + c_2 x^2 + \dots + , \quad |x| &lt; R,
\]
where&nbsp;$R$ is the radius of convergence and it is half the length of the interval $(-R,R)$ containing $x$.
Note that the function $f$ is not obliged to be equal to the associated Maclaurin's series outside the domain $$(-R,R)$.

The Maclaurin series expansion of $\mathrm{f}(x)$ is a series of ascending powers of $x$ of the form

\[
\mathrm{f}(x) = \sum_{n=0}^{\infty} c_n x^n = c_0 + c_1 x + c_2 x^2 + \dots + , \quad |x| < R,
\]

where $R$ is the radius of convergence and it is half the length of the interval $(-R,R)$ containing $x$.

Note that the function $f$ is not obliged to be equal to the associated Maclaurin's series outside the domain $$(-R,R)$.

Definition of Maclaurin's series

Definition of Maclaurin's series