Kdtyjb

It is common (or it used to be) to use a blackboard-bold variant of mu to denote roots of unity in some mathematical papers. However, despite searching (several times, periodically over several years) I have never been able to locate any package or technique that makes this possible, other than using Metafont or possibly hunting through the font definitions to see if it is something I can create a variant of (along the lines of the suggestions in Section 8 of the Comprehensive LaTeX symbol list).

Thus far, I haven't been sufficiently motivated to learn how to do any of this (although it probably would have resulted in a net time savings), and I feel like I cannot be the only person who would have tried. Is anyone aware of an existing way to produce this character?

The mbboard package provides blackboard bold Greek letters, and the letter you want is bbmu. However, I don't know if you like how the symbol looks. (I don't like it, actually.)

The mathbbol package with the bbgreekl option also provides (a possibly nicer version of) bbmu: Use usepackage[bbgreekl]{mathbbol} in the preamble. The disadvantage is that the package also redefines mathbb; see this post for possiblities to avoid this.

Note that lowercase epsilon is typeset with bbespilon (sic).

Edit: I just realised that the mbboard package redefines mathbb, too. If you don't like this, then an easy solution is to load the amssymb package after the mbboard package. This gives you the "usual" blackboard bold letters, and you can still use bbmu and friends.

Another font set that can provide this is MathTime Professional II fonts (mtpro2) from PCTeX. The web site mentions some journals that use these fonts.

The fonts are non-free and, to achieve what is wanted here are, chargeable (the non-free but no-cost 'lite' version does not include the 'blackboard bold italic' and 'holey bold italic' fonts which the two samples below use, using a simple redefinition of mathbb). The outputs are just .pngs of screenprints so don't use these to judge the resolution of the original fonts.

documentclass[12pt]{article}

usepackage[mtpbbi]{mtpro2}

begin{document}

$mathbb{mu} , mathbb{M}$     % assuming 'Mu' = 'M'

end{document}

documentclass[12pt]{article}

usepackage[mtpbbi]{mtpro2}

begin{document}

$mathbb{mu} , mathbb{M}$

end{document}

I also spent a lot of time on the issue and found nothing satisfactory. So I made up my own blackboard bold mu and alpha:

documentclass{minimal}

usepackage{amssymb}

newcommand{Balpha}{mbox{$hspace{0.12em}shortmidhspace{-0.62em}alpha$}}

usepackage{xcolor}

usepackage{graphicx}

newcommand{Bmu}{mbox{$raisebox{-0.59ex}

  {$l$}hspace{-0.18em}muhspace{-0.88em}raisebox{-0.98ex}{scalebox{2}

  {$color{white}.$}}hspace{-0.416em}raisebox{+0.88ex}

  {$color{white}.$}hspace{0.46em}$}{}}

begin{document}

$BalphaquadBmu$

end{document}

This produces

_{(source: uni-muenster.de)}

Just for kicks, you could kludge together your own version which is similar to the symbol in the book you linked in the comments

documentclass{minimal}

usepackage{amsmath}

usepackage{xcolor}

usepackage{graphicx}

newcommand{dmu}{$mu$hspace{-3.2pt}$mu$hspace{-5.7pt}raisebox{-3.06pt}{scalebox{1.6}{$color{white}cdot$}}}

begin{document}

dmu

end{document}

Which produces,