New properties for the Ramanujan R-function

Abstract

In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds for the Ramanujan R-function that improve some previously known results.

Keywords

• ramanujan r-function
• gaussian hypergeometric function
• riemann zeta function
• generalized elliptic integral
• monotonicity
• convexity
• 33c05
• 33b15
• 26a51
• 26d20