Fig. 16

Approximation of a power series derived from the exponential. The power series \(\sum _{k=0}^\infty \frac{z^k}{\left( k+1\right) !}\) is being approximated by \(\sum _{k=0}^n \frac{z^k}{\left( k+1\right) !}\) on the unit disc. For \(z \in \mathbb C \setminus \{0\}\), the power series \(\sum _{k=0}^\infty \frac{z^k}{\left( k+1\right) !}\) is equivalent to the term \(\frac{{e}^z - 1}{z}\)