The exponential function \exp:\mathbb{C}\to\mathbb{C} can be characterized in a variety of equivalent ways.
\exp(z) = \sum_{k = 0}^{\infty} {z^k \over k!} = 1 + z + {z^2 \over 2} + {z^3 \over 6} + {z^4 \over 24} + \cdots .