Patrick, this is a great paper.  It shows the same care you apply to 
maintaining gsl.  The writing is also very clear, and I love the table of 
acronyms :-).  Do you plan to submit for publication in a numerical analysis 
journal, or submit to the arXiv?

The only previous quasi-report had been the ongoing design document that I kept 
going with James and Brian in the early years, but it is a working design doc, 
not anything of the scope you have shown here.

Tiny suggestions: alignment of equation 36 on page 5: "l >= 1" could be moved 
quite a bit to the left.  Maybe an extra & to make it match the start of the l 
>= 1, m > 0.

You might also want to also cite the reference manual (as we ask people to do 
when they use gsl :-) ).  A recent bibtex skeleton on that is the 2019 Network 
Theory edition.

@book{gslteam2019gnuscientificlibrary,
  title={GNU Scientific Library Reference Manual},
  author={Galassi, Mark and Davies, Jim and Theiler, James and Gough, Brian and 
Jungman, Gerard and Alken, Patrick and Booth, Michael and Rossi, Fabrice and 
Ulerich, Rhys},
  year={2019},
  isbn={9780954612078},
  publisher={Network Theory Limited}
}

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