Euler-Type Sums Involving Harmonic Numbers and Binomial Coefficients

被引：1

作者：

Wu, Qiong ^{[1
]}

Xu, Ce ^{[2
]}

Zhou, Jianing ^{[3
]}

机构：

[1] Jiujiang Univ, Coll Sci, Jiujiang 332005, Jiangxi, Peoples R China

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[3] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2024年 / 47卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Euler-type sum; Binomial coefficient; Iterated integral; Multiple harmonic (Star)sum; (Alternating)multiple zeta value; MULTIPLE ZETA VALUES; INTEGRALS;

D O I：

10.1007/s40840-024-01770-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by using iterated integral expression of multiple polylogarithm function, we establish some identities relating multiple harmonic (star) sums and (alternating) multiple zeta values. We then apply these identities and the shuffle relations to evaluate some Euler-type sums involving harmonic numbers and binomial coefficients, such as Sigma(infinity)(n=1) Pi H-p(j=1)n((ij))/(2n+1)(n+r), Sigma(infinity)(n=1) Pi(p)(j=1)H(n)((ij)/)2n+1(kn+k) and some other forms.

引用

页数：18

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