Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: https://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2016, 4(6), 164-167
DOI: 10.12691/tjant-4-6-3
Open AccessArticle

Applications of Z-transform to Some Elemantary Functions in q- and (p,q)-Calculus

Erkan Agyuz1, and Mehmet Acikgoz1

1Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey

Pub. Date: November 05, 2016

Cite this paper:
Erkan Agyuz and Mehmet Acikgoz. Applications of Z-transform to Some Elemantary Functions in q- and (p,q)-Calculus. Turkish Journal of Analysis and Number Theory. 2016; 4(6):164-167. doi: 10.12691/tjant-4-6-3

Abstract

In this paper, we give Z-transform which is a generalization of Laplace transform for solving difference equations some of q and (p,q)-elementary functions, (p, q)- numbers, (p, q)-array and (p, q)-Binom coefficients.

Keywords:
Z-transform q and (p q)-calculus Binom Coefficients trigonometric and exponential functions

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Araci S. and Acikgoz, M, A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers, Advances in Difference Equations 2015, 2015:30.
 
[2]  Araci S., Agyuz E. and Acikgoz M., On a q-analog of some numbers and polynomials, Journal of Inequalities and Applications 2015, 2015:19.
 
[3]  Araci S. and Acikgoz, M and Sen, E., On the von Staudt-Clausenís theorem associated with q-Genocchi numbers, Applied Mathematics and Computation 247, 2014, 780-785.
 
[4]  Chakrabarti, R. and Jagannathan R., A (p, q)-oscillator realization of two-parameter quantum algebras, J. Phys. A: Math. Gen. 24 L711-L718, 1991.
 
[5]  Araci S., Duran U. and Acikgoz M., (ρ, q)-Volkenborn integration, Journal of Number Theory, Vol 171, 18-30, 2017.
 
[6]  Duran U., Post quantum calculus, Master thesis, Gaziantep University, 2016.
 
[7]  Eljaoui E., Melliani S. and Chadli L. S., Solving second-order fuzzy differential equations by the fuzzy Laplace transform method, Advances in Difference Equations, 2015,.2015:66.
 
[8]  Jury, E. I., Theory and Application of the Z-Transform Method. Krieger Publishing Company, New York, 1973.
 
[9]  Kac, V., Cheung P., Quantum Calculus. Springer, New York, 2002.
 
[10]  Kachanov, B., Parametric identi.cation of linear systems using Laplace transform, Automation and Remote Control, 2009,.Vol. 70, Issue 7, pp.1100-1108.
 
[11]  Roy, S.C.D., Difference Equations, Z-transforms and Resistive Ladders, IETE Journal of Education, Vol. 52, Issue 1, 2011.
 
[12]  Sadjang, P. N., On the (p, q)-Gamma and the (p, q)-Beta functions, arXiv:1506.07394, 2015.
 
[13]  Sadjang, P. N., On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas, arXiv:1309.3934, 2013.
 
[14]  Taher B. R., Fetnassi M. E. and Rachidi M., On the z-transform and the nonhomogeneous linear difference equations, Journal of Interdisciplinary Mathematics, Vol.7, Issue 3, 2004.
 
[15]  Yesil, F., Tuglu, N., and Kızılates, C., Some q-Matrices Related To Z-Transform, MSAEN, Vol. 3, 18-24, 2015.