Holomorphic function/Related Articles

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A list of Citizendium articles, and planned articles, about Holomorphic function.
See also changes related to Holomorphic function, or pages that link to Holomorphic function or to this page or whose text contains "Holomorphic function".

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characterized in that there exist holomorphic function : and . [e]

  • Contour plot [r]: Image, that shows a function f of two variables with lines f(x,y)=const in the x,y plane [e]
  • Entire function [r]: is a function that is holomorphic in the whole complex plane. [e]
  • Fundamental Theorem of Algebra [r]: Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a root. [e]
  • Identity function [r]: The function from a set to itself which maps each element to itself. [e]
  • Isolated singularity [r]: A point at which function of a complex variable is not holomorphic, but which has a neighbourhood on which the function is holomorphic. [e]
  • Legendre-Gauss Quadrature formula [r]: the specific approximation of the integral with the sum of N terms, which becomes exact for the polynomial integrand of order < 2N. [e]
  • Limit (mathematics) [r]: Mathematical concept based on the idea of closeness, used mainly in studying the behaviour of functions close to values at which they are undefined. [e]
  • Logarithm [r]: Inverse of exponentiation, as subtraction is the inverse of addition and division is the inverse of multiplication. [e]
  • Mathematical notation [r]: A system of symbolic representations of mathematical objects and ideas. [e]
  • Meromorphic functions [r]: Function of complex variables which is analytic in its domain of definition save at a finite number of points which are poles. [e]
  • Open map [r]: Function between two topological spaces which sends each open set of one to an open set of the other. [e]
  • Pole (complex analysis) [r]: A type of singularity of a function of a complex variable where it behaves like a negative power. [e]
  • Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula. [e]
  • Proof that holomorphic functions are analytic [r]: Add brief definition or description
  • Removable singularity [r]: A singularity of a complex function which can be removed by redefining the function value at that point. [e]
  • Residue (mathematics) [r]: Complex number which describes the behavior of line integrals of a meromorphic function around a singularity. [e]
  • Sequence [r]: An enumerated list in mathematics; the elements of this list are usually referred as to the terms. [e]
  • Special function [r]: Various families of solution functions corresponding to cases of the hypergeometric equation or functions used in the equation's study, such as the gamma function. [e]
  • Superfunction [r]: For given function , solution of equation [e]
  • Taylor series [r]: Representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. [e]
  • Tetration [r]: Holomorphic function characterized in that at integer values of its argument it can be interpreted as iterated exponent. [e]