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Generalized Gudermannian function
Edward Neuman Southern Illinois University and Mathematical Research Institute,
144 Hawthorn Hollow, Carbondale IL 62903, USA
Аннотация:
Wilker and Huygens-type inequalities involving generalized Gudermannian function and its inverse function are established. These results are obtained with the aid of the $p$-version of the Schwab–Borchardt mean. Generalized one-parameter trigonometric and hyperbolic functions play a crucial role in this paper.
Ключевые слова:
Generalized Gudermannian function and its inverse function; generalized trigonometric and generalized hyperbolic functions; Gauss hypergeometric function; $p$-version of the Schwab–Borchardt mean; inequalities.
Поступила в редакцию: 12.01.2018 Исправленный вариант: 26.03.2018 Принята в печать: 11.04.2018
Образец цитирования:
Edward Neuman, “Generalized Gudermannian function”, Пробл. анал. Issues Anal., 7(25):1 (2018), 70–86
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa228 https://www.mathnet.ru/rus/pa/v25/i1/p70
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