Examples
- The Mittag-Leffler star of the complex exponential function defined in a neighborhood of a = 0 is the entire complex plane.
- The Mittag-Leffler star of the complex logarithm defined in the neighborhood of point a = 1 is the entire complex plane without the origin and the negative real axis. In general, given the complex logarithm defined in the neighborhood of a point a ≠ 0 in the complex plane, this function can be extended all the way to infinity on any ray starting at a, except on the ray which goes from a to the origin, one cannot extend the complex logarithm beyond the origin along that ray.
- Any open star-convex set is the Mittag-Leffler star of some complex-analytic function, since any open set in the complex plane is a domain of holomorphy.
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