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Communication Dans Un Congrès Année : 2015

Formulas for Continued Fractions. An Automated Guess and Prove Approach

Sébastien Maulat
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Bruno Salvy

Résumé

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.

Dates et versions

hal-01227259 , version 1 (10-11-2015)

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Citer

Sébastien Maulat, Bruno Salvy. Formulas for Continued Fractions. An Automated Guess and Prove Approach. ISSAC'15, Jul 2015, Bath, United Kingdom. ⟨10.1145/2755996.2756660⟩. ⟨hal-01227259⟩
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