How to stack limits for maths operators?

Question

I have a question on how is it possible to create a \sum with two lower limits directly positioned right underneath each other. I have tried hard and cant seem to get anywhere with it.

Answer 1

I like it better when the i and j are aligned:

This is done by \mathrlap and \mathclap (see this TuGboat article). The article describes the use of some new macro's, including:

\def\mathrlap{\mathpalette\mathrlapinternal} 
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}

add these to your preamble (or load the mathtools package) and you can do something like this:

\[
\sum\limits_{\substack{\mathllap{1\le} i \mathrlap{\le 10} \\ \mathllap{1 \le} j \mathrlap{\le 5}}}^\infty x^i y^j
\]

which produces, in my opinion, a far superior result:

Note that I've added the upper limit \inftyas an example, although I don't see how i and j would be smaller than 10 of 5 and still run up to ininity (ah well, it's just an example).

Answer 2

\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}

\[
  \sum_{\substack{1 \le i \le 10\\ 1 \le j \le 5}}^\infty x^{i} y^{j} \qquad
  \sum_{\mathclap{\substack{1 \le i \le 10\\ 1 \le j \le 5}}}^\infty x^{i} y^{j}
\]  

\end{document}

see also http://www.ctan.org/info/math/voss/mathmode/Mathmode.pdf

Answer 3

Use \substack, as in

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\thispagestyle{empty}

\begin{equation}
  \sum_{\substack{1 \le i \le 10\\ 1 \le j \le 5}} x^{i} y^{j}
\end{equation}

\end{document}

which produces: