# 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.

## 6 Citations

### Quasi‐exactly solvable systems and orthogonal polynomials

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The continued-fraction method of solving classical Fokker?Planck equations has been adapted to tackle quantum master equations of the Caldeira?Leggett type. This was done taking advantage of the…

### Solving spin quantum master equations with matrix continued-fraction methods: application to superparamagnets

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We implement continued-fraction techniques to solve exactly quantum master equations for a spin with arbitrary S coupled to a (bosonic) thermal bath. The full spin density matrix is obtained, so that…

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