(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.

(computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.

(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).

(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.

(computing theory) Capable of computing any recursive function.

(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

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

(mathematics) The general solution of a homogenous linear differential equation.