A Note on the (p,q)-Hermite Polynomials

Authors

Ugur Duran, Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, TR-27310 Gaziantep, TurkeyFollow
Mehmet Acikgoz, Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, TR-27310 Gaziantep, Turkey.Follow
Ayhan Esi, Department of Mathematics, Science and Art Faculty, Adıyaman University, TR-02040 Adıyaman, Turkey.Follow
Serkan Araci, Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey.Follow

Author Country (or Countries)

Turkey.

Abstract

In this paper, we introduce a new generalization of the Hermite polynomials via (p,q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also define a (p,q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p,q)-hyperbolic representations of the (p,q) -Bernstein polynomials. In addition, we obtain a correlation between (p,q)-Hermite polynomials and (p,q)-Bernstein polynomials.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/120122

Recommended Citation

Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan; and Araci, Serkan (2018) "A Note on the (p,q)-Hermite Polynomials," Applied Mathematics & Information Sciences: Vol. 12: Iss. 1, Article 22.
DOI: http://dx.doi.org/10.18576/amis/120122
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss1/22