On monotonicity of ratios of some hypergeometric functions

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.

Authors
Sitnik S.M. 1, 2 , Mehrez K.3
Publisher
Sobolev Institute of Mathematics
Number of issue
1
Language
Russian
Pages
260-268
Status
Published
Volume
13
Year
2016
Organizations
  • 1 Voronezh Institute of the Ministry of Internal Affairs, pr. Patriotov, 53, Voronezh, 394065, Russian Federation
  • 2 Peoples' Friendship University of Russia, M. - Maklaya str., 6, Moscow, 117198, Russian Federation
  • 3 University of Kairouan, Department of Mathematics, ISSAT Kasserine3100, Tunisia
Keywords
Exponential; Hypergeometric functions; Series sections; Turán-type inequalities
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4386/