Applications of a duality between generalized trigonometric and hyperbolic functions

It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinovi\'{c}-Adam...

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Veröffentlicht in:arXiv.org
Hauptverfasser: Miyakawa, Hiroki, Takeuchi, Shingo
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 13.11.2020
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Hyperbolic functions
Trigonometric functions
ISSN:2331-8422
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Abstract It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinovi\'{c}-Adamovi\'{c}-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.
AbstractList It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinovi\'{c}-Adamovi\'{c}-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.
Author Miyakawa, Hiroki
Takeuchi, Shingo
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Snippet It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this...
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Trigonometric functions
Title Applications of a duality between generalized trigonometric and hyperbolic functions
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