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.

Авторы
Sitnik S.M. 1, 2 , Mehrez K.3
Издательство
Sobolev Institute of Mathematics
Номер выпуска
1
Язык
Русский
Страницы
260-268
Статус
Опубликовано
Том
13
Год
2016
Организации
  • 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
Ключевые слова
Exponential; Hypergeometric functions; Series sections; Turán-type inequalities
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4386/