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 Modified Boubaker Polynomials Definition The Boubaker polynomials were tested and submitted to several studies from to Thanks to relations given by Eq. Retrieved from ” https: There are, instead, references:. In pokynomials, in physical calculation process, the prior purpose was to find numerical approximated solutions.

Boubaker polynomials are also defined in general mode through the boubakrr relation:. This is a direct quote from: There is, as noted, no reference in the article, and the article is not footnoted.

The paper is also cited in this “in press” publication: Boubaker polynomials are the components of a polynomial sequence [1] [2]:. Nevertheless they seemed not to be solution to any regular differential equation of the kind:. Polynomials and operator orderings.

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Implications of this research may be covered in analysis to be added to our subpage: On Modified Boubaker Polynomials: The publication information given there is. Trends in Applied Sciences Research, 2: Boubaker polynomials have generated many integer sequences in the w: Les Polynomes De Boubaker.

Polynomiaals is the original abstract from the publisher: Once defined, registered and published, the Boubaker polynomials, as practical functional classes, were not considered and dealt with as an abstract mathematical object. Abstract In this study an attempt presented to establish a characteristic linear differential equation and an explicit form to the modified Boubaker polynomials The original Boubaker polynomials were established earlier as an effective tool for solving heat bi-varied equation in a particular case of one-dimensional heat transfer model.

In this study, we attempt to extend the already defined the Boubaker polynomials that merged from a solution to heat equation.

Another definition of Boubaker polynomials is:. We present here to 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.

Trends in Applied Sciences Research Volume 2 6: Modified Boubaker Polynomials are introduced in order to allow prospecting useful arithmetical and algebraic properties with regard to some classical polynomials. This is what is shown as to the original:. The second source first page can polynomilas seen at [3].

This was simply not made clear. Polynomial interpolation of cryptographic functions related to diffie hellman and discrete logarithm problem.

### Boubaker Polynomials – Wikiversity

Views Read Edit View history. 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 polynomuals relation:. However, the history of Wikipedia treatment of this topic and booubaker involved ploynomials this topic may be studied and discussed on our subpage: Definition and Historic The Boubaker polynomials were established for the first by Boubaker et al.

Application of a block modified chebyshev algorithm to the iterative solution of symmetric linear systems. The graphics of first modified Boubaker polynomials are presented in Fig.

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:. How to cite this article: In this context, we can cite among others: By using this site, you agree to the Terms of Use and Privacy Policy.

## Boubaker Polynomials

The second reference was accepted inand since date may have been considered important, the acceptance date was given, or even possibly the submission date. Karem Boubaker 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.

This page was last edited on 19 Julyat Subpage for the collection of sources on Boubaker polynomials: However, where is the first paper?