The paper deals with three-term recurrence relations for Boubaker and related polynomials, as well as some properties including zero. The Boubaker Polynomials Expansion Scheme for. Solving Applied-physics Nonlinear high-order Differential Equations. 1. Ugur Yücel and. 2. Karem Boubaker. Received August 14, Abstract—Some new properties of the Boubaker polynomials expansion scheme are presented in this paper. It is shown in particular.
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The boubaker polynomials a new function class for solving bi varied second bobaker differential equations. Since the quoted text refers to Boubaker et al, it is referring to the second reference, not the first. On Modified Boubaker Polynomials: The title of the paper is present on Research Gate, with more details, but the actual paper hosted there is the Applied Science paper, not the original one.
Math, Vol 3 Issue 2, — this way:. The second source first page can be seen at . Learn more about original research at Wikiversity.
Boubaker Polynomials – Wikiversity
The graphics of first modified Boubaker polynomials are presented in Fig. The Modified Boubaker Polynomials Definition The Boubaker polynomials were tested and submitted to several studies from to In fact, in physical calculation process, the prior purpose was to find numerical approximated solutions. The Modified Boubaker Polynomials Properties The Modified Boubaker Polynomials Characteristic Differential Equation Oppositely to the early defined Boubaker polynomials, the modified Boubaker polynomials are solution to a second order characteristic equation:.
We introduced in this study a new polynomials class, the modified Boubaker polynomials, derived from an already established polynomial function.
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Nevertheless they seemed not to be solution to any regular differential equation of the kind:. However, the history of Wikipedia treatment of this topic and users involved with this topic may be studied and discussed on our subpage: Implications of this research may be covered in analysis to be added to our subpage: Definition and Historic The Boubaker polynomials were established for the first by Boubaker et al.
Obubaker for the collection of sources on Boubaker polynomials: The early works on polynomials can be attributed to Al-Khawarizmi with his attempt to solve six canonical equations, followed by Omar Al-Khayyam who tried to solves cubics geometrically by intersecting conics Kiltz and Winterhof, This is a direct quote from: Boubaker polynomials are the components of a polynomial sequence  :.
Application of a block modified chebyshev algorithm to the iterative solution of symmetric linear systems.
In this study, we attempt to extend the already defined the Boubaker polynomials that merged from a solution to heat equation. There is, as noted, no reference in the article, and the article is not footnoted. We present here poltnomials the worldwide scientific community, the modified Boubaker polynomials that are closer to mathematical analysis as long as they can be easily subjected to arithmetical and integral analysis.
This is the original abstract from the publisher: Students who pay close attention to detail often find errors in peer-reviewed publications, but such errors may also exist in interpretation.
Polynomials and operator orderings.
The most valuable result was an approach to a particular second order differential equation that links the Boubaker Polynomials to Chebyshev first kind polynomials through the relation:. However, where is the first paper? It shows a boubaked date of March 14,but was not published until June, Karem Boubaker Once defined, registered and published, the Boubaker polynomials, as practical functional classes, were not considered and dealt with as an abstract mathematical object.