Continued fraction as a discrete nonlinear transform

@article{Bender1993ContinuedFA,
  title={Continued fraction as a discrete nonlinear transform},
  author={Carl M Bender and Kimball A. Milton},
  journal={Journal of Mathematical Physics},
  year={1993},
  volume={35},
  pages={364-367}
}
The connection between a Taylor series and a continued fraction involves a nonlinear relation between the Taylor coefficients {an} and the continued fraction coefficients {bn}. In many instances it turns out that this nonlinear relation transforms a complicated sequence {an} into a very simple one {bn}. This simplification is illustrated in the context of graph combinatorics. 
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