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.
https://hal.inria.fr/hal-01227259
Contributeur : Bruno Salvy
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Soumis le : mardi 10 novembre 2015 - 15:47:55
Dernière modification le : vendredi 20 avril 2018 - 15:44:26
Sébastien Maulat, Bruno Salvy. Formulas for Continued Fractions. An Automated Guess and Prove Approach. ISSAC'15, Jul 2015, Bath, United Kingdom. ACM Press, 2015, 〈10.1145/2755996.2756660〉. 〈hal-01227259〉
