Continued Fraction as a Discrete Nonlinear Transform
Carl M. Bender, Kimball A. Milton
Abstract
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 \. We illustrate this simplification in the context of graph combinatorics.
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