Definition of Maclaurin's series

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 $\((-R,R)\).