In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and...

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions...

In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles...

conclusion. Argument may also refer to: Argument (complex analysis), a function which returns the polar angle of a complex number Command-line argument, an item...

moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1...

the argument of the complex number. The complex numbers of absolute value one form the unit circle. Adding a fixed complex number to all complex numbers...

That all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes...

In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest...

Reformation History, journal Argument (complex analysis), the angular component of a complex number or function Argument of a function, a specific input...

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex...

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along...

formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk...

bisector Angular acceleration Angular diameter Angular velocity Argument (complex analysis) Astrological aspect Central angle Clock angle problem Decimal...

In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower...

mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration...

In complex analysis, Liouville's theorem, named after Joseph Liouville (although the theorem was first proven by Cauchy in 1844), states that every bounded...

reaction to this argument: the ability analysis, the acquaintance analysis, and the old fact/new guise analysis. Several objections to the argument have been...

{\displaystyle g_{Y}} . The classical Schwarz lemma is a result in complex analysis typically viewed to be about holomorphic functions from the open unit...

The Meinongian argument is a type of ontological argument or an "a priori argument" that seeks to prove the existence of God. This is through an assertion...

structures. Building on Grimshaw's (1990) analysis of argument structure and events, Alexiadou (2001) studies "complex events," which she refers to as "process...

In mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact...

explicit by analysis. There are several kinds of arguments in logic, the best known of which are "deductive" and "inductive." An argument has one or more...

In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of...

Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The...

mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function...

variable, where the argument is a quaternion (in this case, the sub-field of hypercomplex analysis is called quaternionic analysis). A second instance...

functions. In complex analysis, a function is called analytic in an open set "U" if it is (complex) differentiable at each point in "U" and its complex derivative...

This is a glossary of concepts and results in real analysis and complex analysis in mathematics. In particular, it includes those in measure theory (as...

Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important...

{\displaystyle f(z)} . Laurent series with complex coefficients are an important tool in complex analysis, especially to investigate the behavior of functions...