Sharp Approximations for the Ramanujan Constant.

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 (π a) and polynomials. Some properties of the Riemann zeta function and its related special sums are presented, too. [ABSTRACT FROM AUTHOR]