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Sums, integrals and function names in LaTeX

Write \sum_{i=1}^{n} or \int_{0}^{1} in math mode: the part after _ is the lower limit and the part after ^ the upper one. In a display, the limits of a sum go below and above it.

Sums, products and integrals

Big operators take their limits with _ and ^. In a display formula the limits of \sum, \prod, \bigcup and the like go under and over the symbol; in running text they go to the side, so the line spacing stays even. Integral limits always go to the side.

Big operators in a display

LaTeXOpen in editor
\sum_{i=1}^{n} i = \frac{n(n+1)}{2} \qquad
\prod_{k=1}^{44} \frac{k}{k+1} = \frac{1}{45} \qquad
\int_{0}^{\infty} e^{-x}\,dx = 1 \qquad
\bigcup_{i \in I} A_i
Rendered by Scissor LaTeX: Big operators in a display

\limits after an operator forces the limits above and below, \nolimits puts them to the side. \substack stacks several conditions under a sum.

Limits placement and stacked conditions

LaTeXOpen in editor
\int\limits_{0}^{1} f \qquad \sum\nolimits_{i} a_i \qquad
\sum_{\substack{0 \le i \le n \\ i \ne 44}} a_i \qquad \oint_C \mathbf{F} \cdot d\mathbf{r}
\qquad \iint_D f \, dA

Function names

Function names such as sin, log and max are set upright, with the right spacing, when you use their commands. Typing sin x without the backslash gives italic letters s·i·n, which reads as a product.

Function names

LaTeXOpen in editor
\sin^2 x + \cos^2 x = 1 \qquad \log_2 44 \approx 5.46 \qquad
\lim_{x \to 0} \frac{\sin x}{x} = 1 \qquad \max_{1 \le i \le n} x_i \qquad \det A
Rendered by Scissor LaTeX: Function names

For a name that has no command, use \operatorname{..} in a formula, or define it once in the preamble with \DeclareMathOperator. The starred forms put limits under the name, as for \lim.

Your own operator names

LaTeXOpen in editor
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator*{\argmax}{arg\,max}
\begin{document}
The trace is $\tr A$, and
\[ \hat\theta = \argmax_{\theta} L(\theta), \qquad \operatorname{rank} A = 44. \]
\end{document}

All big operators

Click a copy button to copy the command.

  • \sum
  • \prod
  • \int
  • \iint
  • \iiint
  • \oint
  • \oiint
  • \oiiint
  • \bigodot
  • \bigoplus
  • \bigotimes
  • \bigcup
  • \biguplus
  • \bigsqcup
  • \bigcap
  • \coprod
  • \bigwedge
  • \bigvee
  • \bigdot
  • \bigplus
  • \bigtimes
  • \intop
  • \smallint

All function names

  • \sin
  • \cos
  • \tan
  • \cot
  • \sec
  • \csc
  • \arcsin
  • \arccos
  • \arctan
  • \sinh
  • \cosh
  • \tanh
  • \coth
  • \ln
  • \log
  • \lg
  • \lim
  • \limsup
  • \liminf
  • \hom
  • \det
  • \exp
  • \deg
  • \gcd
  • \lcm
  • \dim
  • \ker
  • \arg
  • \Pr
  • \max
  • \min
  • \argmax
  • \argmin
  • \sup
  • \inf

What does not work

\bigoplus, \bigotimes, \bigodot and \bigcap work with limits; in earlier versions they stopped the whole document (see when the document does not typeset).

Big circled operators and intersections

LaTeXOpen in editor
\bigoplus_{i=1}^{n} V_i \qquad \bigcap_{k} U_k \qquad \bigotimes_{j} W_j

Questions and answers

How do I put the limits of a sum above and below in inline math?

Write \sum\limits_{i=1}^{n}. Use it sparingly: tall inline formulas push the lines of the paragraph apart.

How do I write a double or triple integral?

Use \iint or \iiint, which are spaced better than two \int in a row. \oint gives a contour integral.

How do I write argmax in LaTeX?

Put \DeclareMathOperator*{\argmax}{arg\,max} in the preamble, then write \argmax_{x} f(x). Without the definition, \operatorname*{arg\,max}_{x} does the same in one place.

Every example on this page is typeset by Scissor LaTeX when the site is built. Last updated 2026-11-06.