asymptotic proportionality

Question

Is there a well established notation for asymptotic proportionality by a non-zero and non-unitary constant (for null contant we have little-oh, for unitary constant of asymptotic proportionality we have $\sim$)? Is for example the usual proportionality symbol $\propto$ extended to such use?

Answer 1

I think, if I understood correctly, that $\Theta$ is what you're looking for?

$$f = \Theta(g) \leftrightarrow \exists M>0, (C_1, C_2) \in \mathbb{R}; \forall x>M, C_1<\frac{f(x)}{g(x)}<C_2$$