FPS in action
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Publication:6110898
DOI10.1145/3572867.3572873arXiv2207.01031OpenAlexW4312317477MaRDI QIDQ6110898
Bertrand Teguia Tabuguia, Wolfram Koepf
Publication date: 2 August 2023
Published in: ACM Communications in Computer Algebra (Search for Journal in Brave)
Abstract: Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is "simple" enough. Simplicity is related to the compactness of the formula due to the presence of algebraic numbers: "the smaller, the simpler". This poster showcases the capacity of recent updates on the Formal Power Series (FPS) algorithm, implemented in Maxima and Maple (convert/FormalPowerSeries), to find simple formulas for sequences like those from https://oeis.org/A307717, https://oeis.org/A226782, or https://oeis.org/A226784 by computing power series representations of their correctly guessed generating functions. We designed the algorithm for the more general context of univariate -recursive sequences. Our implementations are available at http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm
Full work available at URL: https://arxiv.org/abs/2207.01031
explicit formulaguessing\(P\)-recursive sequence\(D\)-finite function\(m\)-fold hypergeometric termhypergeometric type power series
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