Homogeneity equation

Summary

The homogeneity equation is the functional equation $f(tx) = t^k f(x)$, required for all positive scalars $t$ and all points $x$. Its solutions are the positively homogeneous functions of degree $k$. They are the functions that scale in a fixed way when all inputs are scaled by the same factor. Homogeneous polynomials of degree $k$ are the basic examples.