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Conference papers

Formulas for Continued Fractions. An Automated Guess and Prove Approach

Sébastien Maulat 1 Bruno Salvy 1
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
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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Contributor : Bruno Salvy <>
Submitted on : Tuesday, November 10, 2015 - 3:47:55 PM
Last modification on : Monday, December 14, 2020 - 5:24:05 PM

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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⟩