摘要
含Stirling数、调和数等特殊组合序列的无穷级数在组合学、数论、算法分析等领域具有重要的应用。利用第一类r-Stirling数的生成函数、特殊函数积分以及广义多重zeta值建立三类含r-Stirling数的含参数无穷级数的表达式,并由此得到很多含第一类Stirling数、调和数及超调和数的级数的值。结果表明:文献中很多相关级数的结论都是这三个一般表达式的特例。在此基础上,进一步利用r-Stirling数的递推关系建立一个广义多重zeta值与经典多重zeta值的关系式,并给出一些特例。
Infinite series involving special combinatorial sequences, such as the Stirling numbers and harmonic numbers, have important applications in combinatorics, number theory, algorithm analysis and some other fields. Using the generating function of the r-Stirling numbers of the first kind, integrals of special functions and generalized multiple zeta values, we establish expressions of three types of parametric infinite series involving the r-Stirling numbers, and on this basis, we obtain the evaluations of some series involving the Stirling numbers of the first kind, harmonic numbers and hyperharmonic numbers. The results show that many series in the literature are particular cases of these three general expressions. Moreover, using the recurrence relation of the r-Stirling numbers, we further establish a relation between the generalized multiple zeta values and the classical multiple zeta values, and provid some particular cases.
作者
马欠欠
王伟平
MA Qianqian;WANG Weiping(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)
出处
《浙江理工大学学报（自然科学版）》
2022年第2期256-261,共6页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
