Abstract and Applied Analysis

p-Trigonometric and p-Hyperbolic Functions in Complex Domain

Petr Girg and Lukáš Kotrla

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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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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

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