Generalized Lamé functions. II. Hyperbolic and trigonometric specializations
نویسندگان
چکیده
منابع مشابه
Inequalities involving generalized trigonometric and hyperbolic functions
The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.
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The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2010, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and parameter convexity and concavity. A number of results have been obtained. This is a survey. Some new refinements, generalizations, applications, ...
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Inequalities involving hyperbolic functions and trigonometric functions are established. Most of the established inequalities can be regarded as the companion inequalities to those obtained by Lazarević, Adamović and Mitrinović and Cusa and Huygens The established results are obtained with the aid of the Schwab-Borchardt mean.
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We establish several sharp inequalities for trigonometric and hyperbolic functions. Our results sharpen some known inequalities. Mathematics subject classification (2010): 26D05, 26D07.
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1999
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532823