  We derive the Taylor polynomial of a function, which is $m$-times
continuously differentiable and positive homogeneous of order $m$. The Taylor
polynomial in $a$ for $f(b)$ of order $m$ in general is a polynomial of order
$m$ in $b-a$. If the given function is positive homogeneous of order $m$, the
Taylor polynomial is a polynomial in $b$ rather than $b-a$, and the order of
all terms is $m$. The result can be applied to powers of homogeneous functions
of order $1$ as well.
