how make a equation a little smaller
with use of the nccmath
package:
\documentclass{article}
\usepackage{nccmath}
\begin{document}
\begin{equation}\medmath{ % <--- reduce equation size for about 20 %
\frac{1}{\psi_{m}}
=\frac{1}{\sum\limits_{k=0}^{n-1}c_{k}\exp\Bigl(\mfrac{-2\pi imk}{n}\Bigr)}
=\frac{1}{\langle V_{m},c \rangle+i\langle U_{m},c\rangle}
=\frac{\langle V_{m},c \rangle-i\langle U_{m},c\rangle}{\langle V_{m},c \rangle^{2}+\langle U_{m},c\rangle^{2}}
}
\end{equation}
or without \verb+\limits+ at \verb+\sum+, i.e. sumation limits are in inline mode:
\begin{equation}\medmath{
\frac{1}{\psi_{m}}
=\frac{1}{\sum_{k=0}^{n-1}c_{k}\exp\Bigl(\mfrac{-2\pi imk}{n}\Bigr)}
=\frac{1}{\langle V_{m},c \rangle+i\langle U_{m},c\rangle}
=\frac{\langle V_{m},c \rangle-i\langle U_{m},c\rangle}{\langle V_{m},c \rangle^{2}+\langle U_{m},c\rangle^{2}}
}
\end{equation}
\end{document}
Edit: added is a case where summation limits consider @Mico comment below.
I suggest that you employ a split
environment inside the equation
environment, split the math material across three lines, and use the =
symbols as the alignment points.
For extra legibility, I would also replace \exp(\frac{-2\pi imk}{n})
with \exp(-2\pi imk/n)
, i.e., use inline-fraction notation in the denominator term of the first fraction expression.
\documentclass{article}
\usepackage{amsmath} % for "split" environment
\begin{document}
\begin{equation}
\begin{split}
\frac{1}{\psi_{m}}
&=\frac{1}{\sum_{k=0}^{n-1}c_{k}\exp(-2\pi imk/n)}\\
&=\frac{1}{\langle V_{m},c\rangle + i\langle U_{m},c\rangle}\\[1ex]
&=\frac{\langle V_{m},c\rangle - i\langle U_{m},c\rangle}%
{\langle V_{m},c\rangle^{2}+ \langle U_{m},c\rangle^{2}}
\end{split}
\end{equation}
\end{document}
I'm not sure what dfrac
is, so I replaced it by frac
and simply used an eqnarray
environment.
\documentclass{article}
\begin{document}
\begin{eqnarray}
\frac{1}{\psi_{m}} &=&\frac{1}{\displaystyle\sum_{k=0}^{n-1}c_{k}
\exp\left(\frac{-2\pi imk}{n}\right)} \nonumber \\
&=& \frac{1}{\langle V_{m},c \rangle+i\langle U_{m},c\rangle} \nonumber \\[7pt]
&=& \frac{\langle V_{m},c \rangle-i\langle U_{m},c\rangle
}{\langle V_{m},c \rangle^{2}+\langle U_{m},c\rangle^{2}}
\end{eqnarray}
\end{document}