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- Title
p-Trigonometric and p-Hyperbolic Functions in Complex Domain.
- Authors
Girg, Petr; Kotrla, Lukáš
- 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·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.
- Subjects
TRIGONOMETRIC functions; HYPERBOLIC functions; DIFFERENTIAL equations; MATHEMATICAL domains; MACLAURIN'S series (Mathematics)
- Publication
Abstract & Applied Analysis, 2016, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2016/3249439