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.
Read more about this topic: Mittag-Leffler Star
Famous quotes containing the words definition, elementary and/or properties:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“If men as individuals surrender to the call of their elementary instincts, avoiding pain and seeking satisfaction only for their own selves, the result for them all taken together must be a state of insecurity, of fear, and of promiscuous misery.”
—Albert Einstein (1879–1955)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)