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Sharp Approximations for the Ramanujan Constant

  • Song-Liang QiuEmail author
  • Xiao-Yan Ma
  • Ti-Ren Huang
Article
  • 6 Downloads

Abstract

In this paper, the authors present sharp approximations in terms of sine function and polynomials for the so-called Ramanujan constant (or the Ramanujan R-function) R(a), by showing some monotonicity, concavity and convexity properties of certain combinations defined in terms of R(a), \(\sin (\pi a)\) and polynomials. Some properties of the Riemann zeta function and its related special sums are presented, too.

Keywords

The Ramanujan constant Monotonicity Convexity and concavity Approximation Functional inequalities The Riemann zeta function 

Mathematics Subject Classification

11M06 33B15 33C05 33F05 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Sci-Tech UniversityHangzhouChina

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