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A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

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 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.