# The Deformed Trigonometric Functions of two Variables

• Volume: 26, Issue: 1-2, page 147-158
• ISSN: 0205-3217

top

## Abstract

top
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.

## How to cite

top

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 - 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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.