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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Bibliographic Details
Published in:arXiv.org
Main Authors: Miyakawa, Hiroki, Takeuchi, Shingo
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 13.11.2020
Subjects:
Hyperbolic functions
Trigonometric functions
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2011.06834