Generalized Chebyshev Polynomials
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 1
Abstract
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 Tn and Un. We show that they are in a Q-vectorial subspace En(x) of Q [x] of dimension n. We establish that the polynomial sequences (h kTn−k)k and (h kUn−k)k, (0 ≤ k ≤ n − 1) are two bases of En(x) for which Tn and Un admit remarkable integer coordinates.
Authors and Affiliations
Mourad Abchiche, Hacéne Belbachir
Keywords
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