On Some Properties of Pell Polynomials

Keywords: Pell polynomials, Expansion coefficients, Product of two polynomials, Exact formula, Power basis

Abstract

This work starts by reviewing the Pell polynomials; its definition and some basic properties. Afterwards, some new properties of such polynomials are investigated. A novel generalization analytical formula is provided defining explicitly the Pell polynomials derivatives of order n in terms of  Pell polynomials themselves. Other explicit formula is concerned with the connection between the Pell polynomials expansion coefficients, this motivates are interest in such polynomials. These formulas are utilized to derive some mainly relationship related with power basis coefficients and Pell polynomials. With the Pell polynomials expansion technique, the powers  are expressed in terms of Pell polynomials and an interesting formula is presented with some detail in the proof. An important general formulation for product of two Pell polynomials is also included in this article. All the representations in this work are obtained by explicit computations. Finally, two examples concern boundary value problem and singular initial value problem are included for applications of the proposed interesting properties of Pell polynomials.

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Author Biographies

Suha SHIHAB, University of Technology - Baghdad - Iraq

She was born in Baghdad in 1970. He had her B.Sc., M.Sc. degrees in Applied Physics from University of Technology, Baghdad (Iraq) in 27/06/1992, 28/12/1995 respectively, and Ph.D. degree in the College of Science, Al-Mustansiriya University Baghdad (Iraq) in 04/10/2005. He has become a Lecturer in 06/03/1999, Assistant professor at 15/03/2002 and Professor at 02/05/2012. She has research gate h-index 3, Scopus h-index 1 and more than 60 published articles inside, outside Iraq. She supervised on many students (Msc. and PHD.) degrees. He was having a many research group on numerical Analysis, optimal Control Systems, and Mathematical Physics. As well as; She have a group for the characterization of semiconducting thin films and nanostructures materials especially the Optical properties with mathematical models produced by different techniques of preparation such as: Spin Coating and Dip Coating (Sol Gel), Sputtering (DC and RF), PLD, chemical bath deposition (CBD) and ....etc. In addition; I have group for the characterization of Ceramic and Polymer materials mathematically produced by many techniques like solid-state and hydrothermal. Authored more than Five books published it in Lambert Academic Publishing in 2012 in Germany. She is reviewer for many international journals. She participate in more than 12 conferences all of them outside Iraq in France, Romania, Algeria and Tunisia.

Mohammed RASHEED, Applied Sciences Department-University of Technology-Baghdad

Mohammed S. Rasheed: He was born in Baghdad in 1971. He had her B.Sc., M.Sc. degrees in Applied Physics from the University of Technology, Baghdad (Iraq) on 03/09/1992, 17/05/1995 respectively, and a Ph.D. degree from the University of Angers, Angers (France) on 12/12/2017. He has become an Assistant professor at 11\11\2018. He has research gate h-index 3, Scopus h-index 3, and more than 30 published articles inside, outside Iraq, and most of them in Clarivate journals. He was having a many research groups on the Preparation and characterization of semiconducting thin films and nanostructures produced by the Spin Coating and Dip Coating (Sol-Gel) technique. As well, He is a member of research groups on the preparation and characterization of semiconducting thin films by chemical bath deposition (CBD) and preparation and characterization of Ceramic and Polymer materials produced by many techniques like solid-state and hydrothermal. Authored one book on the laser communication system and published it in Lambert Academic Publishing in 2012 in Germany. He is a reviewer for two international journals indexed in (Springer & Elsevier). He participates in more than 12 conferences all of them outside Iraq in France, Romania, Algeria, and Tunisia.

Published
2020-12-06
How to Cite
Hassan Aziz, S., SHIHAB, S., & RASHEED, M. (2020). On Some Properties of Pell Polynomials . Al-Qadisiyah Journal of Pure Science, 26(1), Math. 39-. https://doi.org/10.29350/qjps.2021.26.1.1237
Section
Mathematics