On monotonic and logarithmic concavity properties of generalized $k$-Bessel function

Abstract

In this study, our main objective is to determine some monotonic and log-concavity properties of generalized $k$-Bessel function by using its Hadamard product representation and some earlier results on power series. In addition, by using the relationships between Bessel-type special functions and some basic functions, we present some specific examples related to the monotonic and log-concavity properties of some trigonometric and hyperbolic functions.

Keywords

• $k$-Gamma functions
• $k$-Bessel function
• monotonicity
• log-concavity

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