一类含多重调和数的无穷级数的算法  

An Algorithm for a Class of Infinite Series Involving Multiple Harmonic Numbers

作　　者：陈昕 

机构地区：[1]浙江理工大学理学院,浙江 杭州

出　　处：《理论数学》2024年第6期387-398,共12页Pure Mathematics

摘　　要：本文利用部分分式展开及和式变换的方法,为一类含多重调和数的无穷级数建立了递推关系,并证明了此类无穷级数可以用四级的着色多重zeta值表示,并给出了相应的算法及一些特例。In this paper, we use the methods of partial fraction decomposition and transformation of summations to establish a recurrence for a class of infinite series involving multiple harmonic numbers, and prove that such infinite series are expressible in terms of colored multiple zeta values of level four. The corresponding algorithm and some special cases are presented.

关 键 词：多重调和数 多重zeta值 着色多重zeta值 无穷级数 

分 类 号：O17[理学—数学]