# Making the product operator (pi caps) with the extremes above and below the symbol

How can I make the symbol of product operator (pi caps) making the extremes remain the same above and below the symbol? (I do not want the extremes on the right side of the symbol) I wanna write this symbol with that conditions in the simplest possible way.

• This post contains the answer to your question. – apc Mar 30 '16 at 23:00
• I hope you mean with extremes the limits of the operator – user31729 Mar 30 '16 at 23:27
• The problem with above/below limits for inline math is that it screws up the line spacing. Thus, inline (or \textstyle) math puts limits on upper and lower right, as opposed to equation (or \displaystyle) math which places limites above/below. You can override the default configuration by explicitly adding \textstyle or \displaystyle to your math expression. – Steven B. Segletes Mar 31 '16 at 2:27
• @StevenB.Segletes Yes you can, although issuing a \displaystyle declaration in line will also give the larger \prod symbol, which will further destroy good line spacing – Au101 Mar 31 '16 at 9:31

Please be aware that the default behaviour in displaymath mode is for the limits to appear above and below the symbol:

$\prod_{i = 1}^{n} a_{i} \quad \sum_{i = 1}^{n} a_{i} \quad \lim_{n \to \infty} n^{2}$ The only exception to this is integrals:

$\int_{0}^{\infty} x^{2} \, dx$ The default behaviour in inline math mode is for the limits to appear to the side, e.g.

$\prod_{i = 1}^{n} a_{i} \quad \sum_{i = 1}^{n} a_{i} \quad \lim_{n \to \infty} n^{2}$ The reason for this is to avoid irregular spacing between lines and excessive white space.

Compare: With: However, to force the limits to appear above and below in inline math mode you can use \limits as suggested by Christian Hupfer.

$\prod\limits_{i = 1}^{n} a_{i} \quad \sum\limits_{i = 1}^{n} a_{i} \quad \lim\limits_{n \to \infty} n^{2}$ And to force the limits to appear to the side in displaymath mode, you can use \nolimits

$\prod\nolimits_{i = 1}^{n} a_{i} \quad \sum\nolimits_{i = 1}^{n} a_{i} \quad \lim\nolimits_{n \to \infty} n^{2}$ Do you mean this (which is mathematical a little bit incorrect ;-))

The usage of \prod\limits^{upper}_{lower} will produce the product operator with the limits set below and above. Omitting \limits will generate the limits set aside, if \displaystyle isn't used. In displayed equations the limits are set below and above in amsmath, since the sumlimits option is set by default. If this is not desired, use nosumlimits (valid for \sum, \prod, \coprod,\bigoplus and \bigotimes etc operators, but not for integrals)

The 'correct' usage should follow the guideline that limits above and below should be used only in purely mathematical context, not inline with other text, since the line height is stretched here.

\documentclass{article}

\usepackage{mathtools}

\begin{document}
$n! = \prod\limits^{n}_{k=1} k$ versus $n! = \prod^{n}_{k=1} k$

However $n!=\displaystyle\prod^{n-1}_{k=0} (n-k)$ is the better definition
\end{document} • Obvioudly an oversight: $n!=\displaystyle\prod^{n-1}_{k=0} (n-k)$. :-) – GuM Mar 31 '16 at 10:37
• @GustavoMezzetti: Oh, yes, of course. – user31729 Mar 31 '16 at 10:51