Operators
Characters in mathematical mode are usually shown in italics, but sometimes especial function names require different formatting, this is accomplished by using operators defined in LaTeX.
Contents
Introduction
Trigonometrical functions, logarithms, and some others can be written in a document by means of some special commands.
Examples of mathematical operators:
\[
\sin(a + b) = \sin a \cos b + \cos b \sin a
.\]
The commands will print the name of the function in upright instead of italics.
Operators in different contexts
Some operators can take parameters that are handled in a special way, for instance, limits.
Testing notation for limits
\[
\lim_{h \to 0 } \frac{f(x+h)f(x)}{h}
.\]
This operator changes when used alongside
text \( \lim_{h \to 0} (xh) \).
The package amsmath
is needed for the macro \to
; without this package, \rightarrow
has to be used.
Notice how the limit declaration can include a subscript. See the reference guide for a complete list of available operators.
Some languages may add or change some commands, check the main page for languagespecific articles.
Defining your own operators
If you need to add a personalized operator to be displayed in Roman font instead of italics use \DeclareMathOperator
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\arctg}{arctg}
\begin{document}
Userdefined operator for arctangent:
\[
\arctg \frac{\pi}{3} = \sqrt{3}
.\]
\end{document}
The command \DeclareMathOperator
takes two parameters, the first one is the name of the new operator and the second one is the text to be displayed. For this command to work you have to import the package amsmath in the preamble with
\usepackage{amsmath}
The command can be slightly modified if you need that your defined operator uses subscripts, as the \lim
operator, in such case use \DeclareMathOperator*
.
Reference guide
Complete list of mathematical operators
Operator  Renders as 

\cos 

\csc 

\exp 

\ker 

\limsup 

\min 

\sinh 

\arcsin 

\cosh 

\deg 

\gcd 

\lg 

\ln 

\Pr 

\sup 
sup 
\arctan 

\cot 
cot 
\det 

\hom 

\lim 
lim 
\log 

\sec 
sec 
\tan 

\arg 

\coth 

\dim 

\liminf 

\max 

\sin 

\tanh 
Further reading
For more information see
Overleaf guides
 Creating a document in Overleaf
 Uploading a project
 Copying a project
 Creating a project from a template
 Using the Overleaf project menu
 Including images in Overleaf
 Exporting your work from Overleaf
 Working offline in Overleaf
 Using Track Changes in Overleaf
 Using bibliographies in Overleaf
 Sharing your work with others
 Using the History feature
 Debugging Compilation timeout errors
 Howto guides
 Guide to Overleaf’s premium features
LaTeX Basics
 Creating your first LaTeX document
 Choosing a LaTeX Compiler
 Paragraphs and new lines
 Bold, italics and underlining
 Lists
 Errors
Mathematics
 Mathematical expressions
 Subscripts and superscripts
 Brackets and Parentheses
 Matrices
 Fractions and Binomials
 Aligning equations
 Operators
 Spacing in math mode
 Integrals, sums and limits
 Display style in math mode
 List of Greek letters and math symbols
 Mathematical fonts
Figures and tables
 Inserting Images
 Tables
 Positioning Images and Tables
 Lists of Tables and Figures
 Drawing Diagrams Directly in LaTeX
 TikZ package
References and Citations
 Bibliography management with bibtex
 Bibliography management with natbib
 Bibliography management with biblatex
 Bibtex bibliography styles
 Natbib bibliography styles
 Natbib citation styles
 Biblatex bibliography styles
 Biblatex citation styles
Languages
 Multilingual typesetting on Overleaf using polyglossia and fontspec
 Multilingual typesetting on Overleaf using babel and fontspec
 International language support
 Quotations and quotation marks
 Arabic
 Chinese
 French
 German
 Greek
 Italian
 Japanese
 Korean
 Portuguese
 Russian
 Spanish
Document structure
 Sections and chapters
 Table of contents
 Cross referencing sections, equations and floats
 Indices
 Glossaries
 Nomenclatures
 Management in a large project
 Multifile LaTeX projects
 Hyperlinks
Formatting
 Lengths in LaTeX
 Headers and footers
 Page numbering
 Paragraph formatting
 Line breaks and blank spaces
 Text alignment
 Page size and margins
 Single sided and double sided documents
 Multiple columns
 Counters
 Code listing
 Code Highlighting with minted
 Using colours in LaTeX
 Footnotes
 Margin notes
Fonts
Presentations
Commands
Field specific
 Theorems and proofs
 Chemistry formulae
 Feynman diagrams
 Molecular orbital diagrams
 Chess notation
 Knitting patterns
 CircuiTikz package
 Pgfplots package
 Typesetting exams in LaTeX
 Knitr
 Attribute Value Matrices
Class files
 Understanding packages and class files
 List of packages and class files
 Writing your own package
 Writing your own class