Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2016 (2016), Article ID 3249439, 18 pages.
-Trigonometric and -Hyperbolic Functions in Complex Domain
We study extension of -trigonometric functions and and of -hyperbolic functions and to complex domain. Our aim is to answer the question under what conditions on these functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example, . In particular, we prove in the paper that for the -trigonometric and -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 -trigonometric and -hyperbolic functions.
Abstr. Appl. Anal., Volume 2016 (2016), Article ID 3249439, 18 pages.
Received: 28 July 2015
Accepted: 1 December 2015
First available in Project Euclid: 19 May 2016
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Girg, Petr; Kotrla, Lukáš. $p$ -Trigonometric and $p$ -Hyperbolic Functions in Complex Domain. Abstr. Appl. Anal. 2016 (2016), Article ID 3249439, 18 pages. doi:10.1155/2016/3249439. https://projecteuclid.org/euclid.aaa/1463662622