On some properties of Chebyshev polynomials

• Autorzy: Hacène Belbachir , Farid Bencherif
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Chebyshev polynomials; integer coordinates

Kategorie tematyczne

• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11B83: Special sequences and polynomials
• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 121-133

Daty

wydano

2008

otrzymano

2007-04-30

poprawiono

2007-07-24

Twórcy

autor

Hacène Belbachir

• USTHB, Faculty of Mathematics, P.O.Box 32, El Alia, 16111, Algiers, Algeria

autor

Farid Bencherif

• USTHB, Faculty of Mathematics, P.O.Box 32, El Alia, 16111, Algiers, Algeria

Bibliografia

• [1] H. Belbachir and F. Bencherif, Linear recurrent sequences and powers of a square matrix, Integers 6 (A12) (2006), 1-17.
• [2] E. Lucas, Théorie des Nombres, Ghautier-Villars, Paris 1891.
• [3] T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, second edition, Wiley Interscience 1990.

Identyfikatory

DOI

10.7151/dmgaa.1138