On monotonicity of ratios of some \(q\)-hypergeometric functions. (English) Zbl 1474.33068

Summary: 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 Turán-type inequalities. In order to obtain the main results we apply methods developed for the case of classical Kummer and Gauss hypergeometric functions in [the second author, “Inequalities for the exponential remainder”, Preprint; “Conjectures on monotonicity of ratios of Kummer and Gauss hypergeometric functions”, RGMIA, Res. Group. Math. Inequal. Appl. 17, Paper No. 107, 4 p. (2014)].


33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33C05 Classical hypergeometric functions, \({}_2F_1\)
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