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Transformation formulas of finite sums into continued fractions
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-07-29 , DOI: 10.1016/j.jat.2020.105460 Daniel Duverney , Takeshi Kurosawa , Iekata Shiokawa
中文翻译:
有限和转换为连续分数的公式
更新日期:2020-07-29
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-07-29 , DOI: 10.1016/j.jat.2020.105460 Daniel Duverney , Takeshi Kurosawa , Iekata Shiokawa
We state and prove three general formulas allowing us to transform formal finite sums into formal continued fractions and use them to generalize certain expansions in regular continued fractions given by Hone and Varona. As an application, we obtain formulas of transformation of certain series into regular continued fractions. For example, we exhibit a sequence of positive integers which satisfies as well as
中文翻译:
有限和转换为连续分数的公式
我们陈述并证明了三个通用公式,这些公式使我们能够将形式有限和求和转换为形式连续分数,并使用它们来概括Hone和Varona给出的规则连续分数的某些展开。作为应用,我们获得了将某些系列转换为规则连续分数的公式。例如,我们展示一个序列 满足的正整数 以及