Tur\'an type inequalities for confluent hypergeometric functions of the second kind

TL;DR

This paper establishes new tight Turán type inequalities for Tricomi confluent hypergeometric functions of the second kind, improving existing results and deriving new inequalities using integral representations related to the Fisher-Snedecor F distribution.

Contribution

It provides the first derivation of tight Turán inequalities for these functions and offers alternative proofs and new inequalities based on integral representations.

Findings

Improved Turán inequalities for Tricomi confluent hypergeometric functions

New inequalities derived from integral representations

Enhanced understanding of the functions' properties

Abstract

In this paper we deduce some tight Tur\'an type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Tur\'an type inequalities. Moreover, by using these Tur\'an type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Tur\'an type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the study of the infinite divisibility of the Fisher-Snedecor $F$ distribution.