$q$-deformed rationals and $q$-continued fractions. Morier-Genoud, S. and Ovsienko, V. Forum Math. Sigma, 8:e13, 2020.
doi  bibtex   
@Article{	  mor.ovs:20,
  author	= {Morier-Genoud, Sophie and Ovsienko, Valentin},
  title		= {{$q$}-deformed rationals and {$q$}-continued fractions},
  journal	= {Forum Math. Sigma},
  fjournal	= {Forum of Mathematics. Sigma},
  volume	= {8},
  year		= {2020},
  pages		= {e13},
  doi		= {10.1017/fms.2020.9}
}
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