Homogeneous function

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In mathematics, a function f,

is homogeneous of degree p, if

The degree of homogeneity p is a positive integral number.

Examples

Euler's theorem

Let f be differentiable and homogeneous of order p, then

Proof

By the chain rule

From the homogeneity,

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