# Homogeneous function

From Knowino

In mathematics, a function *f*,

is **homogeneous of degree p**, if

The *degree of homogeneity* *p* is a positive integral number.

### [edit] Examples

## [edit] Euler's theorem

Let *f* be differentiable and homogeneous of order *p*, then

### [edit] Proof

By the chain rule

From the homogeneity,

Compare Eqs (1) and (2) for λ = 1 and the result to be proved follows.