EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES

IF 0.2 4区数学 Q4 MATHEMATICS

Mathematical Reports Pub Date : 2023-01-01 DOI:10.59277/mrar.2023.25.75.3.381

SERMIN CAM CELIK, HAYDAR GORAL

引用次数: 0

Abstract

In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series.

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通过三角级数的欧拉-扎吉尔和

在这篇笔记中，我们研究了用三角级数计算欧拉和。人们普遍认为，对于大于7的偶数权值，欧拉和不能用黎曼ζ函数的特殊值来计算。对于偶权，我们将欧拉和的求值化为二重级数的求值和克劳森函数积的积分。我们还用一种基于三角级数的新方法重新计算了奇权的欧拉和。

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

Mathematical Reports MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500. Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.