Some new features of the Boubaker polynomials expansion scheme BPES

On the restricted Chebyshev–Boubaker polynomials

“…Here, r is taken to be an integer parameter (r ∈ Z). When r = 0, we get the modified Chebyshev polynomials U n x 2 [22], while the case r = 3 coincides with the Boubaker polynomials [1,3,7,8,9,12,19,20,24,29,35]. Thus the coefficient array of this family of orthogonal polynomials begins…”

Some properties of Boubaker polynomials and applications

“…According to (4) we conclude that the zeros of the polynomial B n (x) are also eigenvalues of the matrix M n . Also, using Gerschgorin's theorem, it is easy to see that these eigenvalues are in the unit circle |z| < 2 (see also [9]). It is well-known that for orthogonal polynomials on a symmetric interval (−a, a), which satisfy a three-term recurrence relation of the form (3), it can be defined two new polynomial systems which are orthogonal on (0, a 2 ) (cf.…”

“…There are several papers on the so-called Boubaker polynomials and their applications in different problems in physics and other computational and applied sciences (cf. [1,2,3,9] and references therein). Such polynomials are defined in a similar way as Chebyshev polynomials of the first and second kind T n (x) and U n (x), which are orthogonal on (−1, 1) with respect to the weights functions 1/ √ 1 − x 2 and √ 1 − x 2 , respectively.…”

An Attempt to Optimize ZnO-Like TCO Nanolayered Compound Thickness in Terms of a BPES-Related Physical Parameters Pondering

“…The Amlouk-Boubaker optothermal expansivity Ψ AB is a thermophysical parameter defined in precedent studies [35,[43][44][45][46][47][48][49], as a 3D expansion velocity of the transmitted heat inside the material. It is expressed in m 3 s −1 , and calculated by the following:…”

“…where I( λ) AM1.5 is the reference solar spectral irradiance, fitted using the Boubaker polynomials expansion scheme BPES [44][45][46][47]:…”