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Operators

Characters in mathematical mode are usually displayed in italics, but sometimes certain function names require different formatting, which can be achieved by using operators defined in LaTeX.

Trigonometric functions, logarithms, etc., can be written in the document using some special commands, as shown in the following example:

Examples of mathematical operators:
\[
    \sin(a + b) = \sin a \cos b + \cos b \sin a
.\]

The compilation result is as follows:

Operators in Different Environments:​

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Testing notation for limits
\[
    \lim_{h \to 0 } \frac{f(x+h)-f(x)}{h}
.\]
This operator changes when used alongside 
text \( \lim_{h \to 0} (x-h) \).
\end{document}

The compilation result is as follows:

Custom Operators:​

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\arctg}{arctg}
\begin{document}
User-defined operator for arctangent:
\[
    \arctg \frac{\pi}{3} = \sqrt{3}
.\]
\end{document}

The compilation result is as follows:

Quick Reference:​

\cos \csc \exp \ker \limsup \min \sinh \arcsin \cosh \deg \gcd \lg

\ln \Pr \sup \arctan \cot \det \hom \lim \log \sec \tan \arg \coth \dim \liminf \max \sin \tanh