# Typesetting imaginary unit and bessel functions

I know that this issue has been treated in many places, but I have yet to reach something conclusive, hence I am herein seeking your help.

Following the 260.3-1993 - American National Standard Mathematical Signs and Symbols for Use in Physical Sciences and Technology document as well as the Typesetting mathematics for science and technology according to ISO 31/XI guide, I ended up typesetting a certain equation as seen below:

by using the code:

$$\begin{split} W_{m}(kR) &= \mathrm{i}^m \left( \mathrm{j}_m(kR) - \frac{\mathrm{j}_m^{\prime}(kR)} {\mathrm{h}_m^{\prime (2)}(kR)} \mathrm{h}_m^{(2)}(kR)\right) \\ &= \frac{\mathrm{i}^{m+1}} {(kR)^{2} \mathrm{h}_m^{\prime (2)}(kR)}, \end{split} \label{eq:WmkR}$$


with j_m and h_m being the spherical Bessel and Hankel functions.

HOWEVER, the appearance of the imaginary unit as well as the Bessel family functions seem awkward to me, although they comply with the above referenced guidelines documents. Additionally, looking in acoustics books, in wikipedia and a multitude of other resources, I could not spot something that looks like the equation seen above.

The question is, even if this were the correct way of typesetting those functions, would you opt for the usual (albeit probably wrong) formatting of adopting italics?

EDIT (ADDITION): Just to clarify, I find awkward the use of roman letters for the Bessel family functions. Those functions are typeset in italics EVERYWHERE else I looked up.

• Ahm... sorry, but what is wrong with the equation above? I don't understand. Are the subindex in italacs the problem? I need to check the referencies about mathematical orthotypography you use but, as far as I know and as I understand, is common to compose the equations,at least the literals in italics. Only some operators are composed in romans. – Aradnix Dec 14 '13 at 22:23
• @NieldeBeaudrap The mentioned standard is adamant in requiring the imaginary unit to be typeset upright. If one has to comply to it, there's no choice. – egreg Dec 14 '13 at 22:29
• I'd define macros for \mathrm{i}, \mathrm{h} and \mathrm{j} to begin with. Thus you're sure the formatting is uniform (and you can easily change it). – egreg Dec 14 '13 at 22:30
• This is not a TeX problem or a typesetting problem but a matter of choosing notations. ISO 31-11 was replaced by ISO 80000-2 in 2009, but there is no change in the principle that mathematical constants, such as as the imaginary unit, are written in roman (upright) style. You can follow the standard, or you can follow the nonstandard practice of italicizing constants. What matters is what the rules of the publication you are writing for say about. Regarding the functions, it seems that the prime should appear the entire function symbol. – Jukka K. Korpela Dec 14 '13 at 23:03
• FWIW, I can't recall ever reading anything where the Bessel functions are typeset upright, and anything where the imaginary unit is typeset just upright. I have seen many times where the imaginary unit is typeset upright and boldface, like $\mathbf{i}$. In LaTeX I would suggest you define macros for these things in the preamble so that you can change it easily throughout the entire document later on, regardless of what you think of doing now. Your hand may be forced eventually by the house styles of the publisher, if this is a document to be traditionally published. – Willie Wong Dec 16 '13 at 10:05