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A partial function from X to Y is thus a ordinary function that has as its domain a subset of X called the domain of definition of the function. If the domain of definition equals X, one often says that the partial function is a total function. In several areas of mathematics the term "function" refers to partial functions rather than to ...
Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of . [1] In some contexts, a family of sets may be allowed to contain repeated copies of any given member, [ 2 ] [ 3 ] [ 4 ] and in other contexts it may form a proper class .
In mathematics education, a parent function is the core representation of a function type without manipulations such as translation and dilation. [1] For example, for the family of quadratic functions having the general form = + +, the simplest function is =,
In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions.Informally, this means that the functions in the family are not widely spread out, but rather stick together in a somewhat "clustered" manner.
Let X and Y be two metric spaces, and F a family of functions from X to Y.We shall denote by d the respective metrics of these spaces.. The family F is equicontinuous at a point x 0 ∈ X if for every ε > 0, there exists a δ > 0 such that d(ƒ(x 0), ƒ(x)) < ε for all ƒ ∈ F and all x such that d(x 0, x) < δ.
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname {dom} (f)} or dom f {\displaystyle \operatorname {dom} f} , where f is the function.