When substack and array doesn't work

Question

I am trying to write a formula. But both substack and array cannot fulfil my needs (as far as I know how to use them).

The first is how I want it to look like. But I need an i'\neq i below the summation part.

The second is tried with \substack and the third is tried with array and both are unsatisfactory to me. Firstly, the i'\neq i is too big. Secondly, the a_{ii'} is misaligned.

Most preferable would be to maintain the size of the \sum. But if that is not possible, any compromise is okay.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}
\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}
\begin{equation}
\substack{\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}\\i'\neq i}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}
\begin{equation}
\begin{array}{@{}c@{}}\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}\\i'\neq i \end{array}a_{ii'}+ \sum\limits_{i=1}^{I}b_{i}
\end{equation}

\end{document}

Answer 1

You can use \mathop to "define" a math operator that allows stacking of super-/subscripts inside a display:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}

\begin{equation}
\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}
\begin{equation}
\substack{\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}\\i'\neq i}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}
\begin{equation}
\begin{array}{@{}c@{}}\sum\limits_{i=1}^{I}\sum\limits_{i'=1}^{I}\\i'\neq i \end{array}a_{ii'}+ \sum\limits_{i=1}^{I}b_{i}
\end{equation}
\begin{equation}
\mathop{\sum_{i = 1}^I \sum_{i' = 1}^I}_{i' \neq i} a_{ii'} + \sum_{i = 1}^I b_{i}
\end{equation}

\end{document}

Answer 2

Probably an overkill, but an opportunity for \tikzmark:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}

\newcommand\tikzmark[1]{%
  \tikz[remember picture,overlay]\node[inner sep=0pt] (#1) {};}

\begin{document}

\begin{equation}
\sum\limits_{\tikzmark{a}\smash[t]{i=1}}^{I}\sum\limits_{\smash[t]{i'=1}\tikzmark{b}}^{I}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}

\begin{tikzpicture}[remember picture,overlay]
\node[yshift=-6pt] at ( $ (a)!0.5!(b) $ ) {$\scriptstyle i'\neq i$};
\end{tikzpicture}

\end{document}

And since the tikzmark library is available in TeX Live2013, the code simplifies to:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,tikzmark}

\begin{document}

\begin{equation}
\sum\limits_{\tikzmark{a}\smash[t]{i=1}}^{I}\sum\limits_{\smash[t]{i'=1}\tikzmark{b}}^{I}a_{ii'} + \sum\limits_{i=1}^{I}b_{i}
\end{equation}

\begin{tikzpicture}[remember picture,overlay]
\node[yshift=-6pt] at ( $ (pic cs:a)!0.5!(pic cs:b) $ ) {$\scriptstyle i'\neq i$};
\end{tikzpicture}

\end{document}

Since some calculations are performed, the code needs two or three runs to stabilize.