(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.

(mathematical analysis) Any function that is defined for all positive integers, and has values that are either real or complex.

(trigonometry) Any function of an angle expressible as the ratio of two of the sides of a right triangle that has that angle (e.g., sine), or that subtracts 1 from such a ratio or subtracts such a ratio from 1 (e.g., coversed sine).

(computing) an algorithm that generates a numeric, or fixed-size character output from a variable-sized piece of text or other data; used in database table queries, cryptography and in error-checking

(calculus) Of a function, another function, the value of which for any value of the independent variable is the instantaneous rate of change of the given function at that value of the independent variable.

(mathematical analysis) A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers.

(mathematics) A set functions that are analogues of the trigonometric functions for hyperbolic spaces. They can be derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.

(mathematics) a mathematical representation of the relation between the input and output of a linear time-invariant system

(mathematics) A function, the result of the division of two exponential functions, that gives rise to the logistic curve.

(physics) a mathematical function that describes the behaviour of paramagnetic materials and the dielectric properties of insulators