I would like to represent a double sum with i\neq j. So I want two capital sigmas with text i\neq j underneath them. How can I achieve this?
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\mathop allows you to perform operator-related things (like sub-/superscripting underneath/over top in display style) on non-operator symbols:

\documentclass{article}
\begin{document}
\[ \mathop{\sum\sum}_{i\neq j} \]
\end{document}
Using amsmath, it is also possible to declare a new operator, say \sumsum, if you're using this notation on a more frequent basis:
\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\DeclareMathOperator*{\sumsum}{\sum\sum}
\begin{document}
\[ \sumsum_{i\neq j} x_{ij} \]
\end{document}
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Thanks, I ended up doing something similar: \underset{i\neq j}{\sum\sum} – bdeonovic Nov 03 '12 at 22:55
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3@Benjamin But remember that the classes like
\mathopand similar are there for good reasons (spacing, interpretation, ...), therefore it is preffered to use\mathopor\DeclareMathOperator. – yo' Nov 22 '12 at 10:09
\( \sum_{i\ne j}... \)– Andrew Swann Nov 03 '12 at 18:20