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Bounds for confluent Horn function Phi_2 deduced by McKay I_nu Bessel law

The main aim of this article is to derive by probabilistic method new functional and uniform bounds for Horn confluent hypergeometric Phi_2 of two variables and the incomplete Lipschitz-Hankel integral, among others. The main mathematical tools are the representation theorems for the McKay I_nu Bessel probability distribution's CDF and certain known and less known properties of cumulative distribution functions.

Modified Bessel functions of the first kind ; McKay I_nu Bessel distribution ; Confluent Horn Phi_2, Phi_3 functions ; Incomplete Lipschitz-Hankel integral ; Marcum Q function ; Functional bounding inequality

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