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

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...

so one is forced to define it in a multiple-valued sense as a global analytic function. It is common to abuse language and refer to a branch point w 0...

L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and some important conjectures involving L-functions are...

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

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

global spending on big data and business analytics (BDA) solutions is estimated to reach $215.7 billion in 2021. As per Gartner, the overall analytic...

defined. Analytic continuation – Extension of the domain of an analytic function (mathematics) Multivalued function – Generalized mathematical function Densely...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf ⁡ z = 2 π ∫ 0 z e − t 2...

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

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...

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

Analytic philosophy is an analysis focused, broad, contemporary movement or tradition within Western philosophy, especially anglophone philosophy. Analytic...

In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and...

In real algebraic geometry, a Nash function on an open semialgebraic subset U ⊂ Rn is an analytic function f: U → R satisfying a nontrivial polynomial...

ANalytic Application) is an in-memory, column-oriented, relational database management system developed and marketed by SAP SE. Its primary function as...

eigenfunction; this ensures that F has excellent analytic properties, but whether it is actually a complex-analytic function depends on the particular case. The third...

This means that every analytic function is locally represented by its Taylor series. The global form of an analytic function is completely determined...

Tate's theory of global analytic varieties over complete fields In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean...

sets), convex functions (on vector and affine spaces), harmonic and subharmonic functions (on Riemannian manifolds), analytic functions (usually of one...

his zeta function as the Mellin transform of Jacobi's theta function. Riemann used asymptotics of the theta function to obtain the analytic continuation...

z={\frac {1}{\sin z}}.} By using analytic continuation to eliminate removable singularities, meromorphic functions can be added, subtracted, multiplied...

steep as x → ∞, and therefore is not globally Lipschitz continuous, despite being an analytic function. The function f(x) = x2 with domain all real numbers...

it is necessary to analytically continue the function to obtain a form that is valid for all complex s. Because the zeta function is meromorphic, all...

classical local optimization methods. Finding the global minimum of a function is far more difficult: analytical methods are frequently not applicable, and the...

with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero...

one dimensional case, there is no simple analytical formula for the Q-function. Nevertheless, the Q-function can be approximated arbitrarily well as γ...

meta-analytic review, researchers concluded that bilingualism did not enhance executive functioning in adults. The study of executive function in Parkinson's...

functions (as it relies on iterative schemes such as Newton-Raphson). It can be proven that algebraic curves are complete global analytic functions,...

zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar...