Positivity of certain classes of functions related to the Fox H-functions with applications

In this paper, a new set of sufficient conditions are imposed on the parameters of the Fox H-functions, which allow us to conclude that it is non-negative. As applications, some classes of completely monotonic and positive definite functions involving the Fox H-function are established. Some new facts regarding the Fox-Wright functions, including complete monotonicity, logarithmic completely monotonicity and monotonicity of their ratios are discussed.

Automated summary

This paper introduces a new set of conditions for the Fox H-functions, proving that they are non-negative. It also establishes some classes of functions involving the Fox H-function and discusses new facts regarding the Fox-Wright functions.