Properties of generalized (p,q)-elliptic integrals and generalized (p,q)-Hersch-Pfluger distortion function

Abstract

In this paper, we focus on investigating various properties of generalized $ (p, q) $-elliptic integrals and the generalized $ (p, q) $-Hersch-Pfluger distortion function. We establish the complete monotonicity, logarithmic, geometric concavity, and convexity of certain functions involving these generalized integrals and arcsine functions. Additionally, we derive several precise inequalities for the generalized $ (p, q) $-Hersch-Pfluger distortion function, which enhance and extend previous results.

Keywords

• generalized (p， q) -elliptic integrals
• generalized (p， q) -hersch-pfluger distortion function
• convexity
• concavity
• monotonicity
• logarithmic