Holomorphic function/Related Articles

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• Abel function [r]: A strictly increasing continuous function g satisfying $g(f(z))=f(z)+1$ for a given function f. ^[e]
• Biholomorphism [r]: Property of a holomorphic function $f$ from $A\subseteq \mathbb {C}$ to $B\subseteq \mathbb {C}$

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]: For given function $f$, solution $F$ of equation $F(z\!+\!1)=f(F(z))$ ^[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]