(mathematics) Any function whose value is unchanged if the independent variable changes sign i.e. f(x) = f(-x)

(mathematics) The function whose value is zero if its independent variable is negative, and one otherwise.

(mathematics) Any function of a complex variable which is periodic in two directions.

(mathematics) Any function in which an independent variable is in the form of an exponent; they are the inverse functions of logarithms

(mathematical analysis, algebraic geometry) A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.

(mathematics) A function of two, three or n variables which is a solution to any of Laplace's equations

(mathematics) Any function that is a solution of the hypergeometric equation; usually an expansion of an hypergeometric series

(mathematics) A function whose value is always the same as its independent variable, and for which the codomain equals the domain.

(mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x.

(mathematics) Any function, in the calculus of variations, that satisfies the Euler equations