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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On some properties of Chebyshev polynomials

100%
Belbachir H., Bencherif F.
Discussiones Mathematicae - General Algebra and Applications
|
2008
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tom 28
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nr 1
121-133
EN
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 $𝔼_{n}[X]$ 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.
2
Content available remote

Representing derivatives of Chebyshev polynomials by Chebyshev polynomials and related questions

80%
Prodinger H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1156-1160
EN
A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula. Similar formulae are derived for scaled Fibonacci numbers.
3
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A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

70%
Berriochoa E., Cachafeiro A., Díaz J., Martínez E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
156-166
EN
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
4
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On the multivariate transfinite diameter

70%
Bloom T., Calvi J.-P.
Annales Polonici Mathematici
|
1999
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tom 72
|
nr 3
285-305
EN
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
5
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An extension of typically-real functions and associated orthogonal polynomials

61%
Naraniecka I., Szynal J., Tatarczak A.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2011
|
tom 65
|
nr 2
EN
Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties of obtained orthogonal polynomials.
6
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Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

51%
Wituła R., Słota D.
Open Mathematics
|
2006
|
tom 4
|
nr 3
531-546
EN
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.
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