Complex analysis singularity

  • What is the singularity of complex analysis?

    singularity, also called singular point, of a function of the complex variable z is a point at which it is not analytic (that is, the function cannot be expressed as an infinite series in powers of z) although, at points arbitrarily close to the singularity, the function may be analytic, in which case it is called an Oct 4, 2023.

  • What is the singularity of sec 1 z?

    Then sec(1/z) has a non-isolated singularity at 0.
    In another context one considers meromorphic functions (as holomorphic maps to the Riemann sphere).
    From this point of view, poles are not singularities at all, and sec(1/z) has an essential singularity at 0..

  • If an isolated singularity is neither removable nor a pole, it is said to be essential.
    Weierstrass and Casorati proved that an analytic function comes arbitrarily close to every complex number in every neighborhood of an isolated essential singularity.
  • In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate.
    Singularities are often also called singular points.
    Singularities are extremely important in complex analysis, where they characterize the possible behaviors of analytic functions.
Complex analysis. In complex analysis, there are several classes of singularities. These include the isolated singularities, the nonisolated singularities, and  Real analysisComplex analysisIsolated singularitiesFinite-time singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be  Real analysisComplex analysisIsolated singularitiesFinite-time singularity

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