欧拉型和与拉马努金型和的推广

Pub Date : 2020-02-26 DOI:10.2206/kyushujm.75.295

Ce Xu

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引用次数: 4

摘要

定义了一类新的经典二格函数，并建立了它的一些基本恒等式。然后应用所得到的公式，以及Flajolet和Salvy开发的推广工具来研究更一般的欧拉型和。Flajolet和Salvy论文\cite{FS1998}的主要结果是本文主要结果的直接推论。进一步，我们给出了一些涉及双曲级数的ramanujan型恒等式的参数化扩展。考虑了一些有趣的新结果和说明性的例子。

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EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS

We define a new kind of classical digamma function, and establish its some fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler type sums. The main results of Flajolet and Salvy's paper \cite{FS1998} are the immediate corollaries of main results in this paper. Furthermore, we provide some parameterized extensions of Ramanujan-type identities that involve hyperbolic series. Some interesting new consequences and illustrative examples are considered.

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