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.
Petr Girg. Lukáš Kotrla. "-Trigonometric and -Hyperbolic Functions in Complex Domain." Abstr. Appl. Anal. 2016 1 - 18, 2016. https://doi.org/10.1155/2016/3249439