Hurwitz zeta-函数导数的部分和积分表达式及其特殊值  

Integral Expression for Partial Sums of Hurwitz Zeta-function Derivatives and Its Special Values

作　　者：李瑞阳 杨海[1] LI Rui-yang;YANG Hai(Department of Mathematics Xi'an Polytechnic University,Xi'an 710048,Shaanxi)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《商洛学院学报》2025年第2期24-29,共6页Journal of Shangluo University

基　　金：国家自然科学基金项目(11371012);陕西省自然科学基金项目(2021JM443);陕西基础科学研究院科研计划项目(23JSY042)。

摘　　要：研究了Hurwitz zeta-函数及其一阶导数的积分表达式,利用初等数论和解析数论的方法,延伸并扩充了Hurwitz zeta-函数一阶导数的更多积分表达式,不仅得到Hurwitz zeta-函数二阶导数的部分和积分表达式,又得到其特殊值。再将其与完备的Riemann zeta-函数相结合,研究得到Riemann zeta-函数导数的应用及其特殊值。After studying the Hurwitz zeta-function and its first derivative's integral representations,elementary and analytic number theory methods were utilized to extend and expand more integral expressions for the first derivative of the Hurwitz zeta-function.Not only were partial and integral expressions for the second derivative of the Hurwitz zeta-function obtained,but also its special values.Then,by combining it with the complete Riemann zeta-function,the application of the derivative of the Riemann zeta-function and their special values were researched and obtained.

关 键 词：Hurwitz zeta-函数 Riemann zeta-函数 BERNOULLI多项式 特殊值 

分 类 号：O174[理学—数学]