TY - JOUR
A2 - Eloe, Paul W.
AU - Girg, Petr
AU - Kotrla, Lukáš
PY - 2016
DA - 2016/04/27
TI - -Trigonometric and -Hyperbolic Functions in Complex Domain
SP - 3249439
VL - 2016
AB - 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.
SN - 1085-3375
UR - https://doi.org/10.1155/2016/3249439
DO - 10.1155/2016/3249439
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -