On some properties of Chebyshev polynomials

Hacène Belbachir; Farid Bencherif

Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008), p. 121-133 / Harvested from The Polish Digital Mathematics Library

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Résumé

Letting $T_{n}$ (resp. $U_{n}$ ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences ${(X^{k} T_{n - k})}_{k}$ and ${(X^{k} U_{n - k})}_{k}$ for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space $_{n} [X]$ formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also $T_{n}$ and $U_{n}$ admit remarkableness integer coordinates on each of the two basis.

Publié le : 2008-01-01

Zbl 1211.11036

EUDML-ID : urn:eudml:doc:276945

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Hacène Belbachir; Farid Bencherif. On some properties of Chebyshev polynomials. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 121-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1138/

Bibliographie

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[001] [2] E. Lucas, Théorie des Nombres, Ghautier-Villars, Paris 1891.

[002] [3] T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, second edition, Wiley Interscience 1990. | Zbl 0734.41029