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Formulas for Continued Fractions. An Automated Guess and Prove Approach
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
Contributor : Bruno Salvy Connect in order to contact the contributor
Submitted on : Tuesday, November 10, 2015 - 3:47:55 PM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM
Contributor : Bruno Salvy Connect in order to contact the contributor
Submitted on : Tuesday, November 10, 2015 - 3:47:55 PM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM
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