essential singularity

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• Essential singularity — In complex analysis, an essential singularity of a function is a severe singularity near which the function exhibits extreme behavior. Formally, consider an open subset U of the complex plane C, an element a of U , and a meromorphic function f :… …   Wikipedia

• Singularity — may refer to any of a variety of concepts.Mathematics:* Mathematical singularity, a point at which a given mathematical object is not definedIn complex analysis:* Essential singularity, a singularity near which a function exhibits extreme… …   Wikipedia

• Singularity theory — For other mathematical uses, see Mathematical singularity. For non mathematical uses, see Gravitational singularity. In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of …   Wikipedia

• essential — essentially, adv. essentialness, n. /euh sen sheuhl/, adj. 1. absolutely necessary; indispensable: Discipline is essential in an army. 2. pertaining to or constituting the essence of a thing. 3. noting or containing an essence of a plant, drug,… …   Universalium

• Mathematical singularity — In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well behaved in some particular way, such as differentiability. See Singularity theory… …   Wikipedia

• Removable singularity — In complex analysis, a removable singularity of a holomorphic function is a point at which the function is ostensibly undefined, but, upon closer examination, the domain of the function can be enlarged to include the singularity (in such a way… …   Wikipedia

• Microsoft Singularity — Эта статья об операционной системе. О физическом понятии см. Сингулярность. Эта статья или секция статьи содержит информацию о запланированном или ожидаемом будущем программном обеспечении, которое в настоящий момен …   Википедия

• Movable singularity — Solutions to the differential equation subject to the initial conditions y(0)=0, 1 and 2 (red, green and blue curves respectively). The positions of the moving singularity at x= 0, 1 and 4 is indicated by the vertical lines. In the theory of… …   Wikipedia

• Windows Essential Business Server — Windows Essential Business Server …   Википедия

• Weierstrass–Casorati theorem — The Casorati Weierstrass theorem in complex analysis describes the remarkable behavior of meromorphic functions near essential singularities. It is named for Karl Theodor Wilhelm Weierstrass and Felice Casorati.Start with an open subset U of the… …   Wikipedia

• Picard theorem — For the theorem on existence and uniqueness of solutions of differential equations, see Picard s existence theorem. In complex analysis, the term Picard theorem (named after Charles Émile Picard) refers to either of two distinct yet related… …   Wikipedia