Systems of derivatives of polynomials, related to Chebyshev polynomials
نویسندگان
چکیده
منابع مشابه
Polynomials Related to Generalized Chebyshev Polynomials
We study several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal polynomials. Thus, we unify some of well-known results.
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We here give the complete data for the remaining cases deg q = 5, 6, 7, which supplement the paper ([1] Th. Stoll, Decomposition of perturbed Chebyshev polynomials, submitted). This is not supposed to be included in the paper.
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We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that Tn(c cos θ) and Un(c cos θ) are positive definite functions. We further s...
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L(p) = ∫ 1 −1 p(x)x(1− x2)−1/2eiζxdx, ζ ∈ R. Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived. AMS Mathematics Subject Cl...
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The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...
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ژورنال
عنوان ژورنال: Researches in Mathematics
سال: 2015
ISSN: 2664-5009,2664-4991
DOI: 10.15421/241504