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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.
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.
Function spaces play a fundamental role in advanced mathematical analysis, by allowing the use of their algebraic and topological properties for studying properties of functions. For example, all theorems of existence and uniqueness of solutions of ordinary or partial differential equations result of the study of function spaces.
The function in example 1, a removable discontinuity. Consider the piecewise function = {< = >. The point = is a removable discontinuity.For this kind of discontinuity: The one-sided limit from the negative direction: = and the one-sided limit from the positive direction: + = + at both exist, are finite, and are equal to = = +.
An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category. Terminology across fields is quite varied.
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH.
A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).