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- Title
On Some Properties of Pell Polynomials.
- Authors
Aziz, Semaa Hassan; SHIHAB, Suha; RASHEED, Mohammed
- Abstract
This work starts by reviewing the Pell polynomials, its definition and some basic properties. Afterward, some new properties of such polynomials are investigated. A novel generalization analytical formula is constructed explicitly the first derivative of Pell polynomials in terms of Pell polynomials themselves. Another explicit formula is concerned with the connection between the Pell polynomials expansion coefficients; this motivates our 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 1,x,x²,⋯,xn are expressed in terms of Pell polynomials and an interesting formula is presented with some detail in the proof. An important general formulation for the product of two Pell polynomials is also included in this article. Explicit computations obtain all the representations in this work. Finally, two examples concern boundary value problems and singular initial value problems are included for applications of the proposed interesting properties of Pell polynomials.
- Subjects
INITIAL value problems; POLYNOMIALS; BOUNDARY value problems; EXPANSION of solids
- Publication
Al-Qadisiyah Journal of Pure Science, 2021, Vol 26, Issue 1, p39
- ISSN
1997-2490
- Publication type
Article
- DOI
10.29350/qjps.2021.26.1.1237