Sharp Approximations for the Ramanujan Constant

Song-Liang Qiu; Xiao-Yan Ma; Ti-Ren Huang

Sharp Approximations for the Ramanujan Constant

Complex Variables 2018-04-23 v1

Authors: Song-Liang Qiu , Xiao-Yan Ma , Ti-Ren Huang

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

ramanujan identities and series monotone functions zeta values and euler sums

Cite

@article{arxiv.1804.07712,
  title  = {Sharp Approximations for the Ramanujan Constant},
  author = {Song-Liang Qiu and Xiao-Yan Ma and Ti-Ren Huang},
  journal= {arXiv preprint arXiv:1804.07712},
  year   = {2018}
}

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19 pages

Sharp Approximations for the Ramanujan Constant

Abstract

Keywords

Cite

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