Open Access
2016 p-Trigonometric and p-Hyperbolic Functions in Complex Domain
Petr Girg, Lukáš Kotrla
Abstr. Appl. Anal. 2016: 1-18 (2016). DOI: 10.1155/2016/3249439


We study extension of p-trigonometric functions sinp and cosp and of p-hyperbolic functions sinhp and coshp to complex domain. Our aim is to answer the question under what conditions on p these functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example, sin(z)=-i·sinhi·z. In particular, we prove in the paper that for p=6,10,14, the p-trigonometric and p-hyperbolic functions satisfy very analogous relations as their classical counterparts. Our methods are based on the theory of differential equations in the complex domain using the Maclaurin series for p-trigonometric and p-hyperbolic functions.


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Petr Girg. Lukáš Kotrla. "p-Trigonometric and p-Hyperbolic Functions in Complex Domain." Abstr. Appl. Anal. 2016 1 - 18, 2016.


Received: 28 July 2015; Accepted: 1 December 2015; Published: 2016
First available in Project Euclid: 19 May 2016

zbMATH: 1349.33018
MathSciNet: MR3498048
Digital Object Identifier: 10.1155/2016/3249439

Rights: Copyright © 2016 Hindawi

Vol.2016 • 2016
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