Monotonicity of ratios of q-Kummer confluent hypergeometric and q-hypergeometric functions and associated Tur\'an types inequalities

TL;DR

This paper establishes the monotonicity of ratios of q-Kummer confluent hypergeometric and q-hypergeometric functions, linking these properties to Turán-type inequalities using methods adapted from classical hypergeometric functions.

Contribution

It extends the understanding of monotonicity and Turán inequalities to q-analogues of hypergeometric functions using novel analytical methods.

Findings

Proved monotonicity of specific ratios of q-hypergeometric functions.

Established new Turán-type inequalities for these functions.

Connected properties of q-hypergeometric functions with classical cases.

Abstract

In this paper we prove monotonicity of some ratios of $q$--Kummer confluent hypergeometric and $q$--hypergeometric functions. The results are also closely connected with Tur\'an type inequalities. In order to obtain main results we apply methods developed earlier by the authors for the case of classical Kummer and Gauss hypergeometric functions.