In my reading, I've come across the following statement: The function $\Phi(z)$ is said to have degree $\kappa$ at infinity if
$\Phi(z) \sim c_{\kappa}z^{\kappa}+\mathcal{O}(z^{\kappa-1})$
as $z\rightarrow\infty$
What does the $\mathcal{O}$ indicate, and how should I interpret this expression as a whole? For example, my intuition is that $\mathcal{O}$ relates to order, and thus the expression as a whole is saying that the first and second highest order terms dominate for large values of $z$, while the rest can be forgotten.