Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 123-131.

BOUNDS FOR CONFLUENT HORN FUNCTION Φ2 DEDUCED BY MCKAY Iν BESSEL LAW

Dragana Jankov Maširević and Tibor K. Pogány

Department of Mathematics, University of Osijek, 31000 Osijek, Croatia
e-mail: djankov@mathos.hr

Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
Faculty of Maritime Studies, University of Rijeka, 51 000 Rijeka, Croatia
e-mail: pogany.tibor@nik.uni-obuda.hu
e-mail: tibor.poganj@uniri.hr

Abstract.   The main aim of this article is to derive by probabilistic method new functional and uniform bounds for Horn confluent hypergeometric Φ2 of two variables and the incomplete Lipschitz–Hankel integral, among others. The main mathematical tools are the representation theorems for the McKay Iν Bessel probability distribution's CDF and certain known and less known properties of cumulative distribution functions.

2020 Mathematics Subject Classification.   Primary: 26D15, 26D20, 33C70; Secondary: 33E20, 60E05.

Key words and phrases.   Modified Bessel functions of the first kind, McKay Iν Bessel distribution, confluent Horn Φ2, Φ3 functions, incomplete Lipschitz-Hankel integral, Marcum Q function, functional bounding inequality.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/9xn31cd8wy

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