On some properties of hyper-bessel and related functions

Abstract

In this study, by using the Hadamard product representation of the hyper- Bessel function and basic concepts in mathematics we investigate the sign of the hyper- Bessel function x ? J ?d (x) on some sets. Also, we show that the function x ? J ?d (x) is a decreasing function on [0, J ?d ,1), and the function is an increasing function on (0,?), where j ?d ,1 and II ?d denote the first positive zero of the function J ?d (x) and modified hyper-Bessel function, respectively. In addition, we prove the strictly log-concavity of the functions J ?d (x) and J ?d (x) on some sets. Moreover, we give some illustrative examples regarding our main results. © 2019, Işik University, Department of Mathematics.