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A list of Citizendium articles, and planned articles, about Holomorphic function.
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characterized in that there exist holomorphic function g=f^{-1} : f\big(g(z)\big)\!=\!z ~ \forall z \in B ~ and g\big(f(z)\big)\!=\!z ~ \forall z \in A ~ . [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]: A function which subsumes the functionality of a large number of algorithm-based functions in other systems. [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]
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