# Cplx Exponential

Steve Trettel

Medium | Mathematica Notebook |
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The Art | A depiction of the essential singularity of the exponential function at infinity on the Riemann sphere. Drawn using domain coloring, with hue depicting the argument of the image point. |

The Math | The familiar exponential function extends to the complex plane, where it defines a smooth function on the complex plane, but has an essential singularity at infinity, meaning that every neighborhood of infinity maps onto every nonzero complex number infinitely often. These are the most severe singularities in complex functions of 1 variable (compare with removable singularities and poles). |

Categories | Mathematical Illustration, Complex Analysis |