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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).

The exsecant is a little-used trigonometric function defined by excsc(x)=cscx-1, where cscx is the cosecant.

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 definition of a function using a contour integral. Schläfli integrals may be converted into Rodrigues representations.

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

A k-colored graph is a labeled k-colorable graph together with its coloring function (Finch 2003).