I'll give a concrete example and I hope that my general question will be clear.
Say I have three variables, $f$, $g$, $h$, and I know that $f=\mathcal O(x)$, $g=\mathcal O(x^2)$, $h=\mathcal O(x^3)$ ($\mathcal O$-notation) or something of that sort. Now, I want to do a series expansion of expressions involving $f$, $g$, $h$ to a consistent order in $x$. For example, if I write Series[..., {x,0,4}]
I want to keep terms like f^3
and f g
but to throw away terms likef g^2
and g h
.
Is there a simple way to do so?