removable singularity

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• 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

• 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

• Removable — may refer to: * Removable media, computing/electronic data storage * Removable partial denture, dentistry * Removable User Identity Module (R UIM), telecommunicationIn mathematical analysis * Removable discontinuity * Removable set * Removable… …   Wikipedia

• singularity — /sing gyeuh lar i tee/, n., pl. singularities for 2 4. 1. the state, fact, or quality of being singular. 2. a singular, unusual, or unique quality; peculiarity. 3. Math. See singular point. 4. Astron. (in general relativity) the mathematical… …   Universalium

• 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

• removable — removability, removableness, n. removably, adv. /ri mooh veuh beuhl/, adj. 1. that may be removed. 2. Math. a. (of a singularity of a function of a complex variable) noting that the function is not analytic at the point but that the function can… …   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

• 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

• Classification of discontinuities — Jump point redirects here. For the science fiction concept, see jump drive. Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous. If a function is not continuous at a point in… …   Wikipedia

• Residue (complex analysis) — In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for… …   Wikipedia

• Pole (complex analysis) — The absolute value of the Gamma function. This shows that a function becomes infinite at the poles (left). On the right, the Gamma function does not have poles, it just increases quickly. In the mathematical field of complex analysis, a pole of a …   Wikipedia