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Citation - Scopus: 1
On the Orthogonality of the Q-Derivatives of the Discrete Q-Hermite I Polynomials
(IGI Global, 2019) Alwhishi,S.; Adigüzel,R.S.; Turan,M.
Discrete q-Hermite I polynomials are a member of the q-polynomials of the Hahn class. They are the polynomial solutions of a second order difference equation of hypergeometric type. These polynomials are one of the q-analogous of the Hermite polynomials. It is well known that the q-Hermite I polynomials approach the Hermite polynomials as q tends to 1. In this chapter, the orthogonality property of the discrete q-Hermite I polynomials is considered. Moreover, the orthogonality relation for the k-th order q-derivatives of the discrete q-Hermite I polynomials is obtained. Finally, it is shown that, under a suitable transformation, these relations give the corresponding relations for the Hermite polynomials in the limiting case as q goes to 1. © 2020, IGI Global.
Citation - Scopus: 3
Bifurcation in a 3d Hybrid System
(2010) Akhmet,M.U.; Turan,M.
In this paper, we study a 3 dimensional Hybrid system which involves a switching mechanism such that at the moment of switching the differential equation that governs the mode] is changing. We first show that there is a center manifold and based on the results in [2] we show that the system under investigation has a Hopf bifurcation. An appropriate example is constructed to illustrate the theory. © Dynamic Publishers, Inc.