Monotonicity properties and bounds for the complete p-elliptic integrals

Abstract

In the article, we establish some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, and find several sharp bounds for the p-elliptic integrals. Our results are the generalizations and improvements of some previously known results for the classical complete elliptic integrals.

Keywords

• complete elliptic integral
• complete p-elliptic integral
• generalized trigonometric function
• monotonicity
• bound