Applications of a duality between generalized trigonometric and hyperbolic functions II

Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed)...

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Vydáno v:arXiv.org
Hlavní autoři: Miyakawa, Hiroki, Takeuchi, Shingo
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 13.03.2022
Témata:
Hyperbolic functions
Inequalities
Trigonometric functions
ISSN:2331-8422
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Abstract Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.
AbstractList Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.
Author Miyakawa, Hiroki
Takeuchi, Shingo
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Inequalities
Trigonometric functions
Title Applications of a duality between generalized trigonometric and hyperbolic functions II
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