# Multiple-Link Functions

Multiple-Link Functions

Multiple-link functions are functions that have arguments grouped in more than one pair of brackets. They appear in expressions of the type . Definitions of multiple-link functions enable the classification of arguments as either parameters or variables.

f〈p,q,…〉[a,b,…](x,y,…)

Example 1. The identity

L[m,b](x)=mx+b

defines a double-link function, where is a two-parameter family of linear functions.

L

Example 2. A formula for rotating the vector around the axis given by the unit vector through the angle is , involving dot and cross products of vectors.

r

ω

α

Rot[ω,α][r]:=(r·ω)ω+(r-(r·ω)ω)cos(α)+(ω×r)sin(α)

Example 3. The identity

∫f(a,b)=f(x)dx

b

∫

a

defines the definite integral of a function from to which avoids using the bound (or dummy) variable .

f

a

b,

x