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In mathematics, the Boubaker polynomials are a polynomial sequence that arise in an attempt to solve heat bi-varied equation model in a particular case of one-dimensional applied physics model<ref> </ref>.
The Boubaker polynomials have an original and demonstrated monomial term expression, which is a critical part of resolution process:

::<math>B_n(x)=\sum_{p=0}^{\lfloor n/2\rfloor}\frac{(n-4p)}{(n-p)} \binom{n-p}{p} (-1)^p x^{n-2p} </math>

The first few Boubaker polynomials are:

:<math>
\begin{align}
B_0(x) & {} = 1 \\
B_1(x) & {} = x \\
B_2(x) & {} = x^2 2 \\
B_3(x) & {} = x^3 x \\
B_4(x) & {} = x^4-2 \\
B_5(x) & {} = x^5-x^3-3x \\
B_6(x) & {} = x^6-2x^4-3x^2 2 \\
B_7(x) & {} = x^7-3x^5-2x^3 5x \\
B_8(x) & {} = x^8-4x^6 8x^2-2 \\
B_9(x) & {} = x^9-5x^7 3x^5 10x^3-7x \\
& {}\,\,\, \vdots
\end{align}
</math>

Hedi Labiadh et al., Jamel Ghannouchi, and Omotayo Bamidele Awojoyogbe and many specialists worked later on these polynomials. They attempted to establish a Sturm-Liouville shaped characteristic differential equation<ref> </ref> as a guide to establish a rational recurrence relation for the coefficients of the Boubaker polynomials.

Additional reading

(Tunisian magazine)

(Tunisian magazine), also at tunisie7arts.com

References