Types of functions

In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.

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".

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.

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).

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.

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.

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.

In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane.

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.

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.

In mathematics, an analytic function is a function that is locally given by a convergent power series.

In mathematics, a conformal map is a function that preserves angles locally.

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.

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

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.

In mathematics, an empty function is a function whose domain is the empty set ∅.

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.

In mathematics, a binary function also called bivariate function, or function of two variables, is a function that takes two inputs.

In mathematics, a constant function is a function whose (output) value is the same for every input value.

In mathematics, a real-valued function or real function is a function whose values are real numbers.

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.