Properties of generalized (p,q)-elliptic integrals and generalized (p,q)-Hersch-Pfluger distortion function - Chuan-Yu Cai; Qiu-Ying Zhang; Ti-Ren Huang (AIMS Mathematics, 2023)
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.