-Trigonometric and -Hyperbolic Functions in Complex Domain

Petr Girg and Lukáš Kotrla

Abstract and Applied Analysis, 2016, vol. 2016, 1-18

Abstract:

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.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:3249439

DOI: 10.1155/2016/3249439

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