Geodesic
Generalized Chebyshev Polynomials
Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 79-89

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Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind T_n and U_n. We show that they are in a ℚ-vectorial subspace E_n(x) of ℚ[x] of dimension n. We establish that the polynomial sequences (h^kT_n−k)_k and (h^kU_n−k)_k, (0 ≤ k ≤ n − 1) are two bases of 𝔼_n(x) for which T_n and U_n admit remarkable integer coordinates.
Keywords: Chebyshev polynomials, integer coordinates, polynomial bases 
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Abchiche, Mourad; Belbachir, Hacéne. Generalized Chebyshev Polynomials. Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 1, pp. 79-89. http://geodesic.mathdoc.fr/item/DMGAA_2018_38_1_a5/