# How to denote Big O notation in LaTeX like O(n log n)?

Big O is the strander mathematical notation. And this notation is denoted by capital O which is tilted at a slight angle on the right side.  In most cases, you will notice the use of O symbols instead of in various books or documents.

 Symbol Big O notation Type asymptotic Package mismath, physics Commands O(arg), \mathcal{O}(arg) Example O(log n) → O(log n)
\documentclass{article}
\begin{document}
$$O(n^2)$$
$$O(n^c)$$
$$O(g(x))$$
$$O(\max(g_1,g_2))$$
\end{document}

Output :  You have always noticed that backslash is used before the command name. But, in this case, there is no need.

\mathcal{o} will return big o. However, the top-left side of the capital o will remain open in terms of shape.

\documentclass{article}
\begin{document}
$$\mathcal{O}(\log n)$$
$$\mathcal{O}(\log n^c)$$
$$\mathcal{O}(n\log n)$$
$$\mathcal{O}(n!)$$
\end{document}

Output :  Above two methods do not require any package. However, below we will learn two more ways to represent this symbol with the help of mismath and physics package.

## \bigo and \big0 commands in mismath package

Use of mismath package is unknown to many. But, even then, \bigo and \bigO commands can denote this asymptotic notation.

\documentclass{article}
\usepackage{mismath}
\begin{document}
$$\bigo(m^n)$$
$$\bigo(1)$$
$$\bigO(n^3)$$
$$\bigO(2^n)$$
\end{document}

Output :  Little o is used as an asymptotic notation like big o. For example

\documentclass{article}
\usepackage{mismath}
\begin{document}
$$f(n)=\lito(g(n))$$
$$f\in \lito(g)$$
$$\lito \le f(n) <c*g(n)$$
\end{document}

Output :  ## Physics package for \order{arg} command

The advantage of \order command is that the size of symbol will increase and decrease according to the size of the argument.

\documentclass{article}
\usepackage{physics}
\begin{document}
$$\order{<n}$$
$$\order{c^n}$$
$$\order{n\log n}$$
$$\order{\order{h(n)}}$$
$$\order{\frac{n}{k}}$$
\end{document}

Output :  If you want to manually increase the size of the parenthesis, you can use the \big on the right side of the \order command.

\documentclass{article}
\usepackage{physics}
\begin{document}
$$\order\big{\log_b n}$$
$$\order\big{\log_c n}$$
$$\order\big{f(x)}$$
$$\order\Big{\frac{n}{q}} , \order\bigg{\frac{n_i}{q_k}} , \order\Bigg{\frac{n_{ij}}{q_{kj}}}$$
\end{document}

Output :  One thing to keep in mind is that the size of the symbol is fixed by using the * sign with each command in the physics package.

\documentclass{article}
\usepackage{physics}
\begin{document}
$$\order*{n^{\frac{5}{2}}}$$
$$\order*{\frac{n}{k}}$$
$$\order*{f(x)}$$
\end{document}

Output :  