# Index in fraction in exponent in fraction looks wonky

I'm trying to write

$\frac{1}{1+e^{\frac{\varepsilon-\mu}{k_B T}}}$


but it looks really wonky. In particular the B in the subscript is just as big as everything else. I've seen this written in a way that looked nice (without using \exp or writing (...)/(...) instead of \frac{}{}. Is there any nicer way of doing this?

• I would always recommend the exp syntax when the argument get complicated, easier to understand for the reader. Perhaps even combined with / instead of the fraction Jul 15, 2021 at 21:08
• Welcome to TeX.SE.
– Mico
Jul 15, 2021 at 21:18

Consider the following four representations of the same mathematical expression. • The first row is from your posting. TeX knows about scriptstyle (for first-level subscripts and superscripts) and scriptscriptstyle (for second-level subscripts and superscripts) math, but not about scriptscriptscriptstyle. That's why the letter B looks too big relative to k and T.

• The second row succeeds in making the overall expression less tall, by replacing \frac{1}{...} with [...]^{-1}. However, the letter B still looks too big.

• The third row replaces e^{...} with \exp(...). This change, finally, succeeds in getting the relative sizes about right.

• The fourth row replaces frac{a}{b} with (a)/(b), with inline-fraction notation.

In my view, the expressions in rows 3 and 4 both look good.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
&\frac{1}{1+e^{\frac{\varepsilon-\mu}{k_B T}}} \\
&\Bigl[1+e^{\frac{\varepsilon-\mu}{k_B T}}\Bigr]^{-1} \\
&\Bigl[1+\exp\Bigl(\frac{\varepsilon-\mu}{k_B T}\Bigr)\Bigr]^{-1} \\
&\bigl[1+\exp\bigl((\varepsilon-\mu)/(k_B T)\bigr)\bigr]^{-1}
\end{align*}
\end{document}


You can use\tfrac in the exponent (and \mathrm{e}, but that's another problem). Compare:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}

$\frac{1}{1+\mathrm{e}^{\frac{\varepsilon-\mu}{k_B T}}}$

$\frac{1}{1+\mathrm{e}^{\tfrac{\varepsilon-\mu}{k_B T}}}$

\end{document} If you prefer to have a smaller B you can use scalerel package with the command \scaleobj. Here's an example with a scaling factor of 0.7.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{scalerel}
\begin{document}
$\frac{1}{1+e^{\frac{\varepsilon-\mu}{k_{\scaleobj{.7}{B}} T}}}$
\end{document} • +1. Scaling the letter B down seems, to me, preferable to using \tfrac, which in the present expression generates an overly large exponent term that towers over the letter e.
– Mico
Jul 15, 2021 at 21:30