Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function

Abstract

Abstract In the article, we present several new monotonicity properties and bounds involving the generalized Grötzsch ring functions μ a , b $\mu _{a,b}$ in the theory of Ramanujan’s generalized modular equation for 0 < a , b < 1 $0< a, b<1$ . Our results are the variants and extensions of some previously known results.

Keywords

• Gaussian hypergeometric function
• Generalized Grötzsch ring function
• Generalized elliptic integral
• Monotonicity property