In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and...

functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do...

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Higher-order function Y for which Y f = f (Y f)Pages displaying short descriptions of redirect targets Infinite compositions of analytic functions – Mathematical...

functions defined and taking values in complex Banach spaces (or Fréchet spaces more generally), typically of infinite dimension. It is one aspect of...

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Infinite word Decimal expansion Power series Infinite compositions of analytic functions Omega language Helmer, Olaf (January 1938). "The syntax of a...

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sets, according to the behavior of small neighborhoods under iteration. Also see infinite compositions of analytic functions. Other limiting behaviors are...

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

mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic...

analytic solution is unique up to a constant. Functional equation Schröder's equation Böttcher's equation Infinite compositions of analytic functions...

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and a set of functions considered as basic and connected by arithmetic operations (+, −, ×, /, and integer powers) and function composition. Commonly...

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...

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functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine...

Taylor series (is analytic). Holomorphic functions are the central objects of study in complex analysis. Though the term analytic function is often used interchangeably...

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{\displaystyle y\in Y} . Using the composition of functions, this statement can be rewritten to the following equations between functions: f − 1 ∘ f = id X {\displaystyle...

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trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled...

Iterated function Schröder's equation Infinite compositions of analytic functions D.V. Anosov (2001) [1994], "Continuous flow", Encyclopedia of Mathematics...

expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the...