Geodesic
On monotonicity of ratios of some hypergeometric functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 260-268

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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. 
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     author = {S. M. Sitnik and Kh. Mehrez},
     title = {On monotonicity of ratios of some hypergeometric functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {260--268},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a102/}
}
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S. M. Sitnik; Kh. Mehrez. On monotonicity of ratios of some hypergeometric functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 260-268. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a102/