p‐Trigonometric and p‐Hyperbolic Functions in Complex Domain

Petr Girg and Lukáš Kotrla

Abstract and Applied Analysis, 2016, vol. 2016, issue 1

Abstract: 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 · sinh⁡(i · 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.

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2016/3249439

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:3249439

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().