FPS在行动中：一个简单的方法来寻找显式公式交错超几何序列
FPS In Action: An Easy Way To Find Explicit Formulas For Interlaced Hypergeometric Sequences
摘要：
常系数线性递归方程定义有理函数的幂级数系数。然而，人们通常倾向于有一个明确的公式来表示系数序列，只要这样的公式足够“简单”。简单性与公式的紧凑性有关，因为代数数的存在：“越小，越简单”。这张海报展示了在Maxima和Maple（convert/FormalPowerSeries）中实现的形式幂级数（FPS）算法的最新更新的能力，通过计算正确猜测的生成函数的幂级数表示，找到来自https：//oeis.org/A307717、https：//oeis.org/A226782或https://oeis.org/A226784的序列的简单公式。我们设计的算法更一般的情况下，单变量$P$递归序列。我们的实现可在http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm上获得
英文摘要：
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 $P$-recursive sequences. Our implementations are available at http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
