Mittag-Leffler star
In complex analysis, a branch of mathematics, the Mittag-Leffler star of a complex-analytic function is a set in the complex plane obtained by attempting to extend that function along rays emanating from a given point. This concept is named after Gösta Mittag-Leffler. Definition and elementary properties. Formally, the Mittag-Leffler star of a complex-analytic function "ƒ" defined on an open disk "U" in the complex plane centered at a point "a" is the set of all points "z" in the complex plane such that "ƒ" can be continued analytically along the line segment  joining "a" and "z" (see analytic continuation along a curve). It follows from the definition that the Mittag-Leffler star is an open star-convex set (with respect to the point "a") and that it contains the disk "U". Moreover, "ƒ" admits a single-valued analytic continuation to the Mittag-Leffler star. 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"