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

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Abstract

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.

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  1. Department of Mathematics, Kairouan Preparatory Institute For Engineering Studies, University of Kairouan, 3100, Kairouan, Tunisia

    Khaled Mehrez

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  1. Khaled Mehrez
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Correspondence to Khaled Mehrez.

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Dedicated to my children Youssef and Zina.

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Mehrez, K. Positivity of certain classes of functions related to the Fox H-functions with applications. Anal.Math.Phys. 11, 114 (2021). https://doi.org/10.1007/s13324-021-00553-w

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