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Similar questions have been asked before, but my problem is a little different:

\begin{equation}
E_K \approx
\begin{cases}
- \sum\limits_{i = 1}^{N} K_1 \bri \left( \mathbf{m \bri} \cdot \unit{u} \bri \right)^2 V_i & \text{(Uniaxial)} \\
\sum\limits_{i = 1}^{N} [ K_1 \bri \left( m_x^2 \bri m_y^2 \bri + m_y^2 \bri m_z^2 \bri + m_x^2 \bri m_z^2 \bri \right) \\ \qquad + K_2 m_x^2 \bri m_y^2 \bri m_z^2 \bri ] Vi & \text{(Cubic)}
\end{cases} \text{.}
\end{equation}

The above code produces an output as shown below:

enter image description here

The description of the second case is not in the middle. How do I fix this? Also, I should have used \left[...\right] instead of [...]. But, that produces an error.

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It produces an error because they are not on the same line. Use \bigl[...\bigr] instead. –  karlkoeller Jan 14 at 6:31
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2 Answers

You could place the long expression following the second summation symbol in an array structure.

enter image description here

\documentclass{article} 
\usepackage{mathtools} % for 'dcases' environment
\newcommand\bri{(\mathbf{r}_i)}
\newcommand\unit[1]{\hat{\mathbf{#1}}}
\begin{document}\pagestyle{empty}
\begin{equation}
E_K \approx
\begin{dcases}
- \sum_{i = 1}^{N} K_1 \bri \bigl( \mathbf{m \bri} \cdot \unit{u} \bri \bigr)^2 V_i & \text{(Uniaxial)} \\
\begin{array}{l} 
\displaystyle
\smash[b]{\sum_{i = 1}^{N}} 
\Bigl[ K_1 \bri \bigl( m_x^2 \bri m_y^2 \bri \\
\qquad{}+ m_y^2 \bri m_z^2 \bri 
+ m_x^2 \bri m_z^2 \bri \bigr) \\ 
\qquad{}+ K_2 m_x^2 \bri m_y^2 \bri m_z^2 \bri 
\Bigr] V_i 
\end{array}& \text{(Cubic)}
\end{dcases} 
\end{equation}
\end{document}

If you want the second "case" to be split across just two lines, you could do something like the following; note the use of \phantom{-} to line up the two summation symbols:

enter image description here

\documentclass{article} 
\usepackage{mathtools}
\newcommand\bri{(\mathbf{r}_i)}
\newcommand\unit[1]{\hat{\mathbf{#1}}}
\begin{document}\pagestyle{empty}
\begin{equation}
E_K \approx
\begin{dcases}
- \sum_{i = 1}^{N} K_1 \bri \bigl[ \mathbf{m \bri} \cdot \unit{u} \bri \bigr]^2 V_i & \text{(Uniaxial)} \\
\begin{array}{@{}l} 
\displaystyle
\phantom{{}-}
\sum_{i = 1}^{N}
\bigl[ K_1 \bri \bigl( m_x^2 \bri m_y^2 \bri + m_y^2 \bri m_z^2 \bri \\
\qquad{}
+ m_x^2 \bri m_z^2 \bri \bigr) 
+ K_2 m_x^2 \bri m_y^2 \bri m_z^2 \bri 
\bigr] V_i 
\end{array}& \text{(Cubic)}
\end{dcases} 
\end{equation}
\end{document}
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1  
+1. Mico. I stole some code from you ;-) Hope you don't mind. :-) –  Harish Kumar Jan 14 at 7:11
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You can also use aligned. I borrowed the \smash idea from Mico.

\documentclass{article}
\usepackage{amsmath}
\newcommand*{\bri}{(\mathbf{r}_{i})}
\newcommand*{\unit}[1]{\hat{\mathbf{#1}}}
\begin{document}
\begin{equation}
E_K \approx
\begin{cases}
- \sum\limits_{i = 1}^{N} K_1 \bri \left( \mathbf{m \bri} \cdot \unit{u} \bri \right)^2 V_i & \text{(Uniaxial)} \\
\begin{aligned}
&\smash[b]{\sum\limits_{i = 1}^{N}} \big[ K_1 \bri \big( m_x^2 \bri m_y^2 \bri + m_y^2 \bri m_z^2 \bri  \\
&\qquad{}+ m_x^2 \bri m_z^2 \bri \big) \\ 
&\qquad{}+ K_2 m_x^2 \bri m_y^2 \bri m_z^2 \bri \big] Vi\end{aligned}& \text{(Cubic)}
\end{cases} 
\end{equation}
\end{document}

enter image description here

Same thing works for two lines also. Again borrowing from Mico:

\documentclass{article}
\usepackage{amsmath}
\newcommand\bri{(\mathbf{r}_i)}
\newcommand\unit[1]{\hat{\mathbf{#1}}}
\begin{document}\pagestyle{empty}
\begin{equation}
E_K \approx
\begin{cases}
- \displaystyle\sum\limits_{i = 1}^{N} K_1 \bri \bigl[ \mathbf{m \bri} \cdot \unit{u} \bri \bigr]^2 V_i & \text{(Uniaxial)} \\[3ex]
\begin{aligned}
&\phantom{{}-}\smash[b]{\sum_{i = 1}^{N}}
\bigl[ K_1 \bri \bigl( m_x^2 \bri m_y^2 \bri + m_y^2 \bri m_z^2 \bri \\[1ex]
&\qquad{}+ m_x^2 \bri m_z^2 \bri \bigr)
+ K_2 m_x^2 \bri m_y^2 \bri m_z^2 \bri
\bigr] V_i
\end{aligned}& \text{(Cubic)}
\end{cases}
\end{equation}
\end{document}

enter image description here

share|improve this answer
    
I like the space @Mico has managed to set between the two capital sigmas. Do you think you can fix it to look like Mico's? –  Mario S. E. Jan 14 at 17:46
    
@MarioS.E. It is easy \\[3ex]. Fixed. –  Harish Kumar Jan 14 at 22:19
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