Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications

Abstract

Abstract In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties for the functions involving the gamma function and provide the bounds for the error function.

Keywords

• Stolarsky mean
• hyperbolic function
• trigonometric function
• gamma function
• error function
• complete monotonicity