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arXiv · 1507.04203

Formulas for Continued Fractions. An Automated Guess and Prove Approach

Sébastien Maulat·Bruno Salvy
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Abstract

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial conditions. This is used to generate the first few coefficients and from there a conjectured formula. This formula is then proved automatically thanks to a linear recurrence satisfied by some remainder terms. Extensive experiments show that this simple approach and its straightforward generalization to difference and $q$-difference equations capture a large part of the formulas in the literature on continued fractions.

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Sébastien Maulat, Bruno Salvy. 2015-07-15. Formulas for Continued Fractions. An Automated Guess and Prove Approach. https://doi.org/10.1145/2755996.2756660

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