# What does the notation $\mathcal{O}\left(\frac{1}{r^2}\right)$ mean? [duplicate]

I was reading a text about quantum scattering, and I faced a notation I don't understand. The equation is the following: $$\nabla \psi_{\text{scattered}} = \frac{i k f(\theta) e^{ikr}}{r} \mathbf{\hat{r}} + \mathcal{O}\left(\frac{1}{r^2}\right)$$ and I do not know the meaning of the $$\mathcal{O}\left(\frac{1}{r^2}\right)$$ portion.

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Informally, it means that the quantity $$\nabla \psi_{\text{scattered}}$$, when $$r$$ goes to infinity, is equal to $$\frac{ikf(\theta)e^{ikr}}{r}$$ plus some unknown function $$g$$ that does not grow quicker than the function $$r \mapsto \frac{1}{r^2}$$.
From another viewing point, for very large $$r$$ (the very large is essential), if you approximate $$\nabla \psi_{\text{scattered}}$$ with $$\frac{ikf(\theta)e^{ikr}}{r}$$, you know that the error will not grow faster than $$\frac{1}{r^2}$$.