Euler's theorem on homogeneous functions

In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if its argument is multiplied by a factor, then its value is multiplied by some power of this factor.

For example, a homogeneous function of two variables x and y is a real-valued function that satisfies the condition ${\displaystyle f(\alpha x,\alpha y)=\alpha ^{k}f(x,y)}$ for some constant ${\displaystyle k}$ and all real numbers ${\displaystyle \alpha }$. The constant k is called the degree of homogeneity.

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