EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2020-02-26 DOI:10.2206/kyushujm.75.295

Ce Xu

引用次数: 4

Abstract

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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欧拉型和与拉马努金型和的推广

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.