(mathematics) Any of class of special functions, usually denoted as two pairs of functions berₙ(x), beiₙ(x), kerₙ(x) and keiₙ(x) with variable x and given order number n. The former two functions berₙ(x) and beiₙ(x) respectively correspond to the real part and the imaginary part of the Kelvin differential equation's solution that can be expressed with the Bessel function of the first kind Jₙ(x), and the latter kerₙ(x) and keiₙ(x) correspond to those that can be expressed with the modified Bessel function of the second kind Kₙ(x).

(mathematics) Any of a class of functions that are solutions to a particular form of differential equation (a Bessel equation) and are typically used to describe waves in a cylindrically symmetric system.

(mathematics) a function of the type f:V⨯V→V, or more generally, a function of the type f:U_1⨯U_2⨯...⨯U_n→V in which exactly two of the sets Uᵢ are equal to V.

plural of functional group

(mathematics) A function from the real line to a finite subset of the real line.

(mathematics) A function that either never decreases or never increases as its independent variable increases.

(calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).

(mathematics) A function to be maximized or minimized in optimization theory.

(biochemistry, genetics) A genomics branch that measures expression levels of RNAs and proteins to understand biological functions of a set of genes in cells.

(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.