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2 results on '"11M06, 33B15, 33C05, 33F05"'

1. Sharp Approximations for the Ramanujan Constant

Author

Qiu, Song-Liang, Ma, Xiao-Yan, and Huang, Ti-Ren

Subjects
Mathematics - Complex Variables, 11M06, 33B15, 33C05, 33F05
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., Comment: 19 pages

Published
2018

2. Sharp Approximations for the Ramanujan Constant

Author

Xiao-Yan Ma, Song-Liang Qiu, and Ti-Ren Huang

Subjects
Pure mathematics, Mathematics - Complex Variables, Mathematics::General Mathematics, Mathematics::Number Theory, General Mathematics, Numerical analysis, 010102 general mathematics, Monotonic function, 010103 numerical & computational mathematics, 01 natural sciences, Convexity, Ramanujan's sum, Riemann zeta function, Computational Mathematics, symbols.namesake, FOS: Mathematics, symbols, Pi, 11M06, 33B15, 33C05, 33F05, Sine, Complex Variables (math.CV), 0101 mathematics, Constant (mathematics), Analysis, Mathematics
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., Comment: 19 pages

Published
2019
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