摘要
根据不同的应用需求,给出了Ramanujan常数R(a)=-2γ-ψ(a)-ψ(1-a)的几类级数展开式、R(a)与多项式的一些组合的单调性和凹凸性,并利用这些结果获得了R(a)的渐近精确的上下界。运用这些级数展开式,关于R(a)的一些已知结果很容易得到改进。此外还给出了Riemann zeta函数满足的几个恒等式。
Series Expansions and Bounds of the Ramanujan Constant
QIU Songliang , WANG Xiaoyu , LI Qingqing （School of Sciences, Zhejiang Sei-Tech University, Hangzhou 310018, China） Abstract. In this paper, the authors present several kinds of series expansions of the Ramanujan constant R（a）=-2γ-ψ（a）-ψ（1-a）,and monotonicity and convexity properties of certain combinations defined in terms of R（a） and polynomials, according to different application needs. By these results, several asymptotically sharp upper and lower bounds are obtained for R（a）, and some known related results can be easily improved. In addition, several identities satisfied by the Riemann zeta function are provided. Key words： Ramanujan constant; psi function; series expansion; monotonicity and convexity; inequalities
出处
《浙江理工大学学报（自然科学版）》
2017年第1期104-109,共6页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
基金
supported by the National Natural Science Foundation of China(NSFC)(1171307)
