(mathematical analysis) Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ.

(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) A printed tabulation of selected values of a function corresponding to selected independent variables; e.g. a table of logarithms.

(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

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

(mathematics) Any function whose values are points

(computing) Any of a set of subroutines that perform standard mathematical functions included in a programming language; either included in a program at compilation time, or called when a program is executed

(mathematics) A function where the independent variable is raised to a particular real number power.