The Deformed Trigonometric Functions of two Variables

Marinkovic, Sladjana, Stankovic, Miomir, and Mulalic, Edin. "The Deformed Trigonometric Functions of two Variables." Mathematica Balkanica New Series 26.1-2 (2012): 147-158. <http://eudml.org/doc/281397>.

@article{Marinkovic2012,
abstract = {MSC 2010: 33B10, 33E20Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine and cosine functions and analyze their various properties. We give series expansions of these functions, formulas which have their similar counterparts in the classical trigonometry, and interesting difference and differential properties.},
author = {Marinkovic, Sladjana, Stankovic, Miomir, Mulalic, Edin},
journal = {Mathematica Balkanica New Series},
keywords = {exponential function; trigonometric functions; deformed exponential function},
language = {eng},
number = {1-2},
pages = {147-158},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {The Deformed Trigonometric Functions of two Variables},
url = {http://eudml.org/doc/281397},
volume = {26},
year = {2012},
}

TY - JOUR
AU - Marinkovic, Sladjana
AU - Stankovic, Miomir
AU - Mulalic, Edin
TI - The Deformed Trigonometric Functions of two Variables
JO - Mathematica Balkanica New Series
PY - 2012
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 26
IS - 1-2
SP - 147
EP - 158
AB - MSC 2010: 33B10, 33E20Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine and cosine functions and analyze their various properties. We give series expansions of these functions, formulas which have their similar counterparts in the classical trigonometry, and interesting difference and differential properties.
LA - eng
KW - exponential function; trigonometric functions; deformed exponential function
UR - http://eudml.org/doc/281397
ER -