Monotonicity properties and inequalities related to generalized Grötzsch ring functions

Abstract

In the paper, the authors present some monotonicity properties and some sharp inequalities for the generalized Grötzsch ring function and related elementary functions. Consequently, the authors obtain new bounds for solutions of the Ramanujan generalized modular equation.

Keywords

• gaussian hypergeometric function
• generalized hersch–pfluger distortion function
• sharp inequality
• generalized grötzsch ring function
• generalized modular equation
• primary 33e05
• secondary 26a48
• 26d15