# The Deformed Trigonometric Functions of two Variables

Marinkovic, Sladjana; Stankovic, Miomir; Mulalic, Edin

Mathematica Balkanica New Series (2012)

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

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topMarinkovic, 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 -

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