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The function f(x)=1-2|x|^(1/2) for x in [-1,1]. The natural invariant is rho(y)=1/2(1-y).

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.

The motion along a phase curve as a function of time (Tabor 1989, p. 14).

The catacaustic of the quadrifolium with arbitrary radiant point is a complicated function. A few example are illustrated above.

A recurrence relation between the function Q arising in quota systems, Q(n,r)=Q(n-1,r-1)+Q(n-1,r).

A function is termed regular iff it is analytic and single-valued throughout a region R.