(mathematics) A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X.

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

(mathematics) Any function whose value is the solution of a polynomial; an element of a subring of the ring of all functions over an integral domain, which subring is the smallest to contain all the constant functions and also the identity function. (If the polynomial is multivariate then there is a different identity function corresponding to each variable.)

(mathematics) Any function whose value repeats after the regular addition of a period to its independent variable; i.e., a function ƒ such that, for some positive constant p, ƒ(x + p) = ƒ(x) for all x.

(mathematical analysis) A function whose codomain is a topological space and domain is a measurable space, with the property that the inverse image of every open set in its codomain is a measurable set in its domain.

(mathematics) A generalization of the indicator function for a fuzzy set which assigns a truth value (0 or 1) to each element.

(logic) An expression containing algebraic symbols that serve to represent words or other elements of a sentence or proposition

(mathematics) A function of a complex variable obtained by differentiating the logarithm of a gamma function; the digamma function / (physics) The Schrödinger wave function

(mathematics) a meromorphic function

(statistics) Any function used to obtain a set of samples from a given population