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Problemy Analiza — Issues of Analysis, 2018, Volume 7(25), Issue 1, Pages 70–86
DOI: https://doi.org/10.15393/j3.art.2018.4310 (Mi pa228) 		 
Generalized Gudermannian function

Edward Neuman

Southern Illinois University and Mathematical Research Institute, 144 Hawthorn Hollow, Carbondale IL 62903, USA
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DOI: https://doi.org/10.15393/j3.art.2018.4310
Abstract: 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.
Keywords: Generalized Gudermannian function and its inverse function; generalized trigonometric and generalized hyperbolic functions; Gauss hypergeometric function; $p$-version of the Schwab–Borchardt mean; inequalities.
Received: 12.01.2018
Revised: 26.03.2018
Accepted: 11.04.2018
Bibliographic databases:
Document Type: Article
UDC: 517.51, 517.52, 517.58
MSC: 26E60, 26D07, 26D20
Language: English
Citation: Edward Neuman, “Generalized Gudermannian function”, Probl. Anal. Issues Anal., 7(25):1 (2018), 70–86
Citation in format AMSBIB
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\paper Generalized Gudermannian function
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\vol 7(25)
\issue 1
\pages 70--86
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