Some properties of the difference between the Ramanujan constant and beta function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Qiu, Song-Liang¹  Ma, Xiao-Yan¹  Huang, Ti-Ren¹ 

[1] Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

关键词: The Ramanujan constant;    Beta function;    Monotonicity and convexity;    Functional inequalities;    Power series;    The Riemann zeta function;   

DOI  :  10.1016/j.jmaa.2016.08.043

来源: Elsevier

【 摘 要 】

The authors present the power series expansions of the function R(a) - B(a) at a = 0 and at a = 1/2, show the monotonicity and convexity properties of certain familiar combinations defined in terms of polynomials and the difference between the so-called Ramanujan constant R(a) and the beta function B(a) = B(a,1 a), and obtain asymptotically sharp lower and upper bounds for R(a) in terms of B(a) and polynomials. In addition, some properties of the Riemann zeta function zeta(n), n epsilon N, and its related sums are derived. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free