Typesetting functions: italics or non italics?

Question

I've been typesetting all my functions in non-italics (even for $f(x)$), but am not sure if this is the correct convention. This website suggests that generic functions (e.g., $f(x), g(x)$ should be in italics and only ones with fixed meaning should not (e.g., $\sin(x)$). What if I give the function a fixed meaning (e.g., $F(x)$ always mean XXX in the text). What convention does everyone use?

Answer 1

There are various, and often conflicting, typographical conventions for virtually everything under the sun, including mathematical typesetting. It's true that some typographical conventions are more widely observed than others, depending on which country and typographical tradition you feel you are associated with. However, there is no universal convention for math typesetting, beyond possibly [??] the convention that the = symbol should always signify "equality" or "is equal to" -- in some properly defined sense, of course.

Rather than committing to any one given math style, you may want to look into typesetting your documents under XeLaTeX and/or LuaLaTeX. That way, you can make use of the unicode-math package, which offers four [yes, 4] different "math styles" that govern the way non-bold lowercase and uppercase Latin and Greek letters are typeset. They are:

• ISO: italic (aka sloped) shape for all Latin and Greek letters, both uppercase and lowercase.

• TeX (maybe should be called "Knuth"?): italic shape for all Latin letters (both uppercase and lowercase); italic lowercase Greek letters; upright uppercase Greek letters.

• french: italic lowercase Latin letters; upright uppercase Latin letters; upright lowercase and uppercase Greek letters.

• upright: upright shape for all Latin and Greek letters, both uppercase and lowercase.

I'm pretty confident that these four styles manage to cover the vast majority of conventions one may run into "in the wild". However, I wouldn't be surprised if there were some math typesetting conventions out there, somewhere, that do not conform to one of these four styles. Do please let me know if you run across such a deviant math style...

The following table shows how these styles affect the "look" of lowercase and uppercase Latin and Greek letters.

The important thing to do is to use as little visual formatting as possible and, instead, to rely on LaTeX and the unicode-math package to do the tedious job for you of making the typeset mathematics adhere to the chosen style.

The unicode-math package also offers three options for the bold-style criterion: ISO, TeX, and upright; see section 5.2 of the package's user guide for detailed information. To use the ISO style for regular-weight letters and the upright style for bold letters, you'd type

\setmathfont{Stix Two Math}[math-style=ISO,bold-style=upright]

---

You asked a separate question:

What if I give the function a fixed meaning (e.g., $F(x)$ always mean XXX in the text)?

The typographic issue worth noting isn't that F could happen to represent only one specific function -- at least in your usage of F. The typographic issue at stake is that F is very much a generic symbol; as such, the way it should get typeset should very much depend on the math style you employ. In contrast, \sin can only ever mean one thing -- unless you want to assign a non-standard meaning to \sin, in which case you will have well earned the unforgiving and everlasting enmity of your readers...

---

Here's the code that gave rise to the screenshot shown above.

\documentclass{article}
\usepackage{booktabs,unicode-math}
\setmainfont{Stix Two Text} % or some other suitable text font
\newcommand\blurb{$abc \quad y=f(x) \quad ABC \quad \sigma\phi\psi \quad \Sigma\Phi\Psi$}
\begin{document}
\begin{tabular}{@{}ll@{}}
math style & output \\
\midrule
ISO & \setmathfont{Stix Two Math}[math-style=ISO]\blurb \\
TeX & \setmathfont{Stix Two Math}[math-style=TeX]\blurb \\
french & \setmathfont{Stix Two Math}[math-style=french]\blurb  \\
upright & \setmathfont{Stix Two Math}[math-style=upright]\blurb \\
\end{tabular}
\end{document}