3

Consider the following beamer code:

\documentclass{beamer}
\usepackage{mathtools, amsmath}
\begin{document}
\begin{frame}
    \vspace{-1.5cm}
    Result:
    \begin{align*}
    \pi_1(k, i\w) &=- \left( \frac12 \log\frac{D^2+\w^2}{\w^2} - \tan^{-1}\frac{D}{\w} \right) \\
    \pi_2(k,i\w) &= \left( \frac12 \log\frac{D^2+\w^2}{\w^2} + \tan^{-1}\frac{D}{\w} \right) \\
    \Pi_1(k, i\w) &= \begin{dcases}
     -\frac{\e_{q,R}^2}{\e_{q,R}^2 + \w^2}, & q \sim 0 \\
    {\scriptstyle
    \begin{multlined} 
    \frac12 \left[ -\frac14 \log((\e_{q'R}-2D)^2 + \w^2) - \frac14 \log((\e_{q'R}+2D)^2 + \w^2) + \frac12 \log(\e_{q'R}^2 +\w^2) \right.\\
    \left.\quad -\frac12 i \left( \tan^{-1} \frac{\e_{q'R}-2D}{\w} + \tan^{-1} \frac{\e_{q'R}+2D}{\w} \right) \right]
    \end{multlined}
}
    , & q \sim 2k_F     
    \end{dcases}.
    \end{align*}
\end{frame}
\end{document}

The result is an overfull equation as in the picture: enter image description here

Why the \scriptstyle does not work, and how can I fix it?

3

multlined uses \displaystyle. On the other hand, \scriptstyle is bad because fractions will have numerators and denominators in \scriptscriptstyle so the subscripts will turn out to be too big. Better splitting the last parenthesis and use one more line, all in \textstyle.

\documentclass{beamer}
\usepackage{mathtools, amsmath}

\newcommand{\e}{\epsilon}
\newcommand{\w}{\omega}

\begin{document}
\begin{frame}
    Result:
    \begin{align*}
    \pi_1(k, i\w) &=- \left( \frac12 \log\frac{D^2+\w^2}{\w^2} - \tan^{-1}\frac{D}{\w} \right) \\
    \pi_2(k,i\w) &= \left( \frac12 \log\frac{D^2+\w^2}{\w^2} + \tan^{-1}\frac{D}{\w} \right) \\
    \Pi_1(k, i\w) &= \begin{dcases}
     -\frac{\e_{q,R}^2}{\e_{q,R}^2 + \w^2}, & q \sim 0 \\
      \begin{aligned}[b]
      \textstyle
      \frac12 \Bigl[
        &\textstyle - \frac14 \log((\e_{q'R}-2D)^2 + \w^2) \\
        &\textstyle - \frac14 \log((\e_{q'R}+2D)^2 + \w^2) \\
        &\textstyle + \frac12 \log(\e_{q'R}^2 +\w^2) \\
        &\textstyle - \frac12 i \tan^{-1} \frac{\e_{q'R}-2D}{\w} \\
        &\textstyle - \frac12 i \tan^{-1} \frac{\e_{q'R}+2D}{\w}
    \Bigr],
    \end{aligned}
    & q \sim 2k_F     
    \end{dcases}.
    \end{align*}
\end{frame}
\end{document}

enter image description here

I left the trailing dot, but, as you see, it's hanging from nowhere.

| improve this answer | |
4

For fun, with use the rcases defined in the mathtools package:

enter image description here

\documentclass{beamer}
\usepackage{mathtools}
\newcommand*{\w}{\omega}
\newcommand*{\e}{\epsilon}

\begin{document}

\begin{frame}
Result:
    \begin{align*}
    \pi_1(k, i\w) & = -\left(\frac{1}{2} \log\frac{D^2+\w^2}{\w^2} - \tan^{-1}\frac{D}{\w} \right) \\
    \pi_2(k, i\w) & =  \left(\frac{1}{2} \log\frac{D^2+\w^2}{\w^2} + \tan^{-1}\frac{D}{\w} \right) \\
    \Pi_1(k, i\w) &= \\
    \MoveEqLeft[2.4]{\begin{dcases}
     -\frac{\e_{q,R}^2}{\e_{q,R}^2 + \w^2}\raisebox{2.4pt}{ ,} & q \sim 0 \\
     \begin{rcases}
    \frac{1}{2}\biggl[
        - \frac{1}{4} \log\bigl((\e_{q'R}-2D)^2 + \w^2\bigr) \\
    \quad\,
        - \frac{1}{4} \log\bigl((\e_{q'R}+2D)^2 + \w^2\bigr)
            + \frac{1}{2} \log\bigl(\e_{q'R}^2 +\w^2\bigr) \\
    \quad\,
        - \frac{1}{2} i \Bigl( \tan^{-1} \frac{\e_{q'R}-2D}{\w} + \tan^{-1} \frac{\e_{q'R}+2D}{\w} \Bigr) \biggr]
    \end{rcases}
    , & q \sim 2k_F
    \end{dcases}}
    \end{align*}
\end{frame}

\end{document} 
| improve this answer | |
3

I don't think you need \scriptstyle, which is not very readable. I suggest to split the dcases environment into 4 lines, and nest it in a fleqn environment, from nccmath(to be loaded before mathtools). Also, I used the medium-sized fractions from the latter package for the fractionary coefficients:

\documentclass{beamer}
\usepackage{nccmath, mathtools}
\newcommand*{\w}{\omega}
\newcommand*{\e}{\epsilon}

\begin{document}

\begin{frame}
    \vspace{-0.5cm}
    Result:
\begin{fleqn}
    \begin{align*}
    \pi_1(k, i\w) &=- \left( \mfrac12 \log\frac{D^2+\w^2}{\w^2} - \tan^{-1}\frac{D}{\w} \right) \\
    \pi_2(k,i\w) &= \left( \mfrac12 \log\frac{D^2+\w^2}{\w^2} + \tan^{-1}\frac{D}{\w} \right) \\
    \Pi_1(k, i\w) &= \\
    \MoveEqLeft[3]{\begin{dcases}
     -\frac{\e_{q,R}^2}{\e_{q,R}^2 + \w^2}, & q \sim 0 \\
     \begin{aligned}
    \mfrac12\biggl[ & -\mfrac14 \log((\e_{q'R}-2D)^2 + \w^2) \\
     & - \mfrac14 \log((\e_{q'R}+2D)^2 + \w^2)+ \mfrac12 \log(\e_{q'R}^2 +\w^2) \\
     & -\mfrac12 i \left( \tan^{-1} \frac{\e_{q'R}-2D}{\w} + \tan^{-1} \frac{\e_{q'R}+2D}{\w} \right) \biggr]
    \end{aligned}
    , & q \sim 2k_F
    \end{dcases}.}
    \end{align*}
\end{fleqn}
\end{frame}

\end{document} 

enter image description here

| improve this answer | |

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