an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions...

mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily...

analytic function is often used interchangeably with "holomorphic function", the word "analytic" is defined in a broader sense to denote any function...

As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis...

analytic functions, unlike for complex analytic (that is, holomorphic) functions, these statements fail to hold. For example, consider the function f...

branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds...

quasi-analytic class of functions is a generalization of the class of real analytic functions based upon the following fact: If f is an analytic function on...

In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of...

analysis, the analytic capacity of a compact subset K of the complex plane is a number that denotes "how big" a bounded analytic function on C \ K can...

holomorphic functions are analytic and vice versa. Among the corollaries of this theorem are the identity theorem that two holomorphic functions that agree...

bounded analytic function can become Analytic continuation, a technique to extend the domain of definition of a given analytic function Analytic manifold...

complex analytic variety or complex analytic space is a generalization of a complex manifold that allows the presence of singularities. Complex analytic varieties...

the field dealing with the properties of these functions is called several complex variables (and analytic space), which the Mathematics Subject Classification...

global analytic function is a generalization of the notion of an analytic function which allows for functions to have multiple branches. Global analytic functions...

of its Taylor series, even if its Taylor series is convergent. A function is analytic at a point x if it is equal to the sum of its Taylor series in some...

example of a function that is differentiable but not locally Lipschitz continuous. The exponential function e x {\displaystyle e^{x}} is analytic, and hence...

In SQL, a window function or analytic function is a function which uses values from one or multiple rows to return a value for each row. (This contrasts...

The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic...

(3rd ed.). W. H. Freeman. ISBN 978-0-7167-2877-1. "Residue of an analytic function", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Weisstein, Eric...

\operatorname {Re} (s)>1} , and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory and has applications...

important sub-class of analytic expressions, which contain a finite number of applications of well-known functions. Unlike the broader analytic expressions, the...

antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions. A function of...

mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable...

processing, an analytic signal is a complex-valued function that has no negative frequency components.  The real and imaginary parts of an analytic signal are...

sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging...

theorems about the range of an analytic function. They are named after Émile Picard. Little Picard Theorem: If a function f : C → C {\textstyle f:\mathbb...

transcendental functions such as the exponential function and trigonometric functions. It is the starting point of the study of analytic functions, and is fundamental...

result about analytic continuation of a complex-analytic function to a larger set. The idea is that one can extend a complex-analytic function (from here...

Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem...

for the related function discussed in the Non-analytic smooth function article. This function can be interpreted as the Gaussian function exp ⁡ ( − y 2...