On monotonicity of ratios of some $q$-hypergeometric functions

Authors

  • Khaled Mehrez University of Kairouan, Department of Mathematics, ISSAT Kasserine 3100, Tunisia Author
  • Sergei M. Sitnik Peoples' Friendship University of Russia, M. - Maklaya str., 6, Moscow, 117198, Russia Author

Keywords:

Kummer functions, Gauss hypergeometric functions, $q$-Kummer confluent hypergeometric functions, $q$-hypergeometric functions, Turán type inequalities

Subjects:

33D15

Abstract

In this paper, we prove monotonicity of some ratiosof $q$-Kummer confluent hypergeometric and $q$-hypergeometricfunctions. The results are also closely connected with Turántype inequalities. In order to obtain main results we applymethods developed for the case of classical Kummer and Gausshypergeometric functions in [S.M. Sitnik, Inequalities for theexponential remainder, preprint, Institute of Automation andControl Process, Far Eastern Branch of the Russian Academy ofSciences, Vladivostok 1993 (in Russian)] and [S.M. Sitnik,Conjectures on Monotonicity of Ratios of Kummer and GaussHypergeometric Functions, RGMIA Research Report Collection 17(2014), Article 107].

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Published

2016-07-15

Issue

Vol. 68 No. 3 (2016): Vol. 68, Issue 3

Section

Articles

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Copyright (c) 2016 Authors retain copyright to their work.

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This work is licensed under a Creative Commons Attribution 4.0 International License.