Types of functions

2017-07-27T17:52:06+03:00[Europe/Moscow] en true Weierstrass function, Arithmetic function, Convex function, Elementary function, Functional (mathematics), Holomorphic function, Window function, Entire function, Harmonic function, Vector-valued function, Analytic function, Conformal map, Identity function, Periodic function, Univalent function, Empty function, Zonal spherical function, Binary function, Constant function, Real-valued function, Morphism of algebraic varieties flashcards Types of functions
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  • Weierstrass function
    In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.
  • Arithmetic function
    In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function f(n) defined on the set of natural numbers (i.e., positive integers) that "expresses some arithmetical property of n".
  • Convex function
    In mathematics, a real-valued function defined on an interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.
  • Elementary function
    In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations (+ – × ÷), exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of nth roots).
  • Functional (mathematics)
    In mathematics, and particularly in functional analysis and the calculus of variations, a functional is a function from a vector space into its underlying field of scalars.
  • Holomorphic function
    In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
  • Window function
    In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.
  • Entire function
    In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane.
  • Harmonic function
    In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplace's equation, i.
  • Vector-valued function
    A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.
  • Analytic function
    In mathematics, an analytic function is a function that is locally given by a convergent power series.
  • Conformal map
    In mathematics, a conformal map is a function that preserves angles locally.
  • Identity function
    In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
  • Periodic function
    In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
  • Univalent function
    In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.
  • Empty function
    In mathematics, an empty function is a function whose domain is the empty set ∅.
  • Zonal spherical function
    In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K-invariant vector in an irreducible representation of G.
  • Binary function
    In mathematics, a binary function also called bivariate function, or function of two variables, is a function that takes two inputs.
  • Constant function
    In mathematics, a constant function is a function whose (output) value is the same for every input value.
  • Real-valued function
    In mathematics, a real-valued function or real function is a function whose values are real numbers.
  • Morphism of algebraic varieties
    In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.