(game theory) A mathematical function that assigns a real number to every element of the outcome space in a way that captures the agent's preferences over both simple and compound lotteries.

(computing theory) Capable of computing any recursive function.

(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.

(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).

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

(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) 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

(organic chemistry) A specific grouping of elements that is characteristic of a class of compounds, and determines some properties and reactions of that class.

(mathematics) A function which, when applied a given number of times, equals another given function.

(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.