Mittag-Leffler Star - Uses

Uses

Any complex-analytic function ƒ defined around a point a in the complex plane can be expanded in a series of polynomials which is convergent in the entire Mittag-Leffler star of ƒ at a. Each polynomial in this series is a linear combination of the first several terms in the Taylor series expansion of ƒ around a.

Such a series expansion of ƒ, called the Mittag-Leffler expansion, is convergent in a larger set than the Taylor series expansion of ƒ at a. Indeed, the largest open set on which the latter series is convergent is a disk centered at a and contained within the Mittag-Leffler star of ƒ at a