# Category: Meromorphic functions

Ahlfors theory
Ahlfors theory is a mathematical theory invented by Lars Ahlfors as a geometric counterpart of the Nevanlinna theory. Ahlfors was awarded one of the two very first Fields Medals for this theory in 193
Value distribution theory of holomorphic functions
In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. It tries to get quantitative measures of the number of times a function f(z) assumes a va
Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining fur
Nevanlinna theory
In the mathematical field of complex analysis, Nevanlinna theory is part of thetheory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna. Hermann Weyl called it "one of the few great
Rational function
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coe
Gamma function
In mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function
Wiman-Valiron theory
Wiman-Valiron theory is a mathematical theory invented by Anders Wiman as a tool to study the behavior ofarbitrary entire functions. After the work of Wiman, the theory was developed by other mathemat
Transcendental function
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcen
Removable singularity
In complex analysis, a removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point in such a way that the r
Algebraic function
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms,
Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined as for and its analytic continuation elsewhere.
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. (Mor
Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated points, which