# Why the summation is printed like this?

The values of the upper and lower limits of a summation are usually printed below and above sigma. But I find TeX something very unusual. How to correct this?

Here is the MWE:

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
<\mu_{m}> = \frac{\sum_{-J}^{J}{-g\mu_{\beta}M_{J}B.\exp{\left(\frac{-g\mu_{\beta}M_{J}B}{kT}\right)}}}{\sum_{-J}^{J}{\exp{\left(\frac{-g\mu_{\beta}M_{J}B}{kT}\right)}}}
\end{align}
\end{document}


The output:

-
Don't use <>. Use \langle \rangle instead. – Sigur Jul 19 '14 at 16:49
It's because you have the sums in a fraction. Use \sum\limits_{-J}^{J} to change the limit position. – Paul Gessler Jul 19 '14 at 16:49
@Sigur \langle \rangle, makes it soooo thin – subham soni Jul 19 '14 at 16:54
OK, but < is a relation symbol and \langle is a delimiter. They are different in some sense and the space around them are different. – Sigur Jul 19 '14 at 16:56

LaTeX by default uses scriptstyle for sums inside fractions. You can change the sums to displaystyle like this:

$\langle \mu_{m} \rangle = \frac{{\displaystyle \sum_{-J}^{J}}{-g\mu_{\beta}M_{J}B.\exp{\left(\frac{-g\mu_{\beta}M_{J}B}{kT}\right)}}} {{\displaystyle \sum_{-J}^{J}}{\exp{\left(\frac{-g\mu_{\beta}M_{J}B}{kT}\right)}}}$


PLEASE, use \langle \rangle instead of < >. Here's the output:

-
\displaystyle is not recommended here. See @Paul's comment above. The ideal would be \sum\limits. – Sigur Jul 19 '14 at 16:57
Also, \left and \right add certain unwanted space, better \Bigl( and \Bigr). And one more, if you want to use the . as a multiplication symbol (binary operator), wether you define a command, or use \mathbin{.}. – Manuel Jul 19 '14 at 17:02
@Sigur Err... ok. Displaystyle also makes the sigma bigger, but maybe it looks better this way. – Jairo Bochi Jul 19 '14 at 17:02
@JairoBochi I too would use \sum\limits precisely in order to avoid big summation signs; you might show both alternatives. The period is never used for multiplication in math, as far as I know. Either \cdot or nothing. In this case nothing is surely better. – egreg Jul 19 '14 at 20:04
I think the best solution is to use the nccmath package, and \medopsum\limits_{-J}^{J} to have medium-sized` sum operator. – Bernard Jul 19 '14 at 21:03