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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 260–268
DOI: https://doi.org/10.17377/semi.2016.13.019 (Mi semr669) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Real, complex and functional analysis

On monotonicity of ratios of some hypergeometric functions

S. M. Sitnikab, Kh. Mehrezc

a Peoples' Friendship University of Russia, M. - Maklaya str., 6, Moscow, 117198, Russia
b Voronezh Institute of the Ministry of Internal Affairs, pr. Patriotov, 53, Voronezh, 394065, Russia
c University of Kairouan, Department of Mathematics, ISSAT Kasserine 3100, Tunisia
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DOI: https://doi.org/10.17377/semi.2016.13.019
Abstract: In the preprint [1] one of the authors formulated some conjectures on monotonicity of ratios for exponential series sections. They lead to more general conjecture on monotonicity of ratios of Kummer hypergeometric functions and were not proved from 1993. In this paper we prove some conjectures from [1] for Kummer hypergeometric functions and its further generalizations for Gauss and generalized hypergeometric functions. The results are also closely connected with Turán–type inequalities for special functions.
Keywords: hypergeometric functions, exponential, series sections, Turán–type inequalities.
Received November 16, 2015, published April 8, 2016
Bibliographic databases:
Document Type: Article
UDC: 517.521.1
MSC: 33A45,26D15
Language: Russian
Citation: S. M. Sitnik, Kh. Mehrez, “On monotonicity of ratios of some hypergeometric functions”, Sib. Èlektron. Mat. Izv., 13 (2016), 260–268
Citation in format AMSBIB
\Bibitem{SitMeh16}
\by S.~M.~Sitnik, Kh.~Mehrez
\paper On monotonicity of ratios of some hypergeometric functions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 260--268
\mathnet{http://mi.mathnet.ru/semr669}
\crossref{https://doi.org/10.17377/semi.2016.13.019}
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