I have come across the notation
$$...+\ O_R(x)$$
where $R$ is any positive real number, and $R<2$. What is the term big $O_R$ of $x$ referring to?
2026-05-14 17:47:18.1778780838
Big-$O$ notation definition.
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Usually, $A = B + O_R(x)$ means that for all $R$, there exists $C_R > 0$ such that for all $x$, $$|A-B| \leq C_R |x|.$$ Notice that $A$ and $B$ can be functions of $R$ and $x$. Depending on the context, the inequality may be required only for $x$ lying in some set, for $x$ large enough, for $x$ near enough $0$, etc.