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

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...

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

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

most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example)...

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

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...

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

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...

real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be...

and results in real analysis and complex analysis in mathematics. See also: list of real analysis topics, list of complex analysis topics and glossary...

In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative...

distinguished from complex analysis, which deals with the study of complex numbers and their functions. The theorems of real analysis rely on the properties...

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

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...

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

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...

{\displaystyle 0} is near to very small numbers. The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances...

ISBN 978-0-521-48364-3 Rao, Murali; Stetkær, Henrik (1991). Complex Analysis: An Invitation : a Concise Introduction to Complex Function Theory. World Scientific. p. 113...

complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis...

boundary. In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane...

In complex analysis, the open mapping theorem states that if U {\displaystyle U} is a domain of the complex plane C {\displaystyle \mathbb {C} } and f...

by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis, the complex...

periodic. The Riemann mapping theorem, one of the profound results of complex analysis, states that any non-empty open simply connected proper subset of C...

Complex segregation analysis (CSA) is a technique within genetic epidemiology to determine whether there is evidence that a major gene underlies the distribution...

analytic. Consequently, in complex analysis, the term analytic function is synonymous with holomorphic function. Real and complex analytic functions have...

heading. As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that...

studied but not distances; it can be studied as the complex plane using techniques of complex analysis; and so on. A curve is a 1-dimensional object that...

Look up Analysis or analysis in Wiktionary, the free dictionary. Analysis is the process of observing and breaking down a complex topic or substance into...

the partial derivatives and directional derivatives exist. In complex analysis, complex-differentiability is defined using the same definition as single-variable...