Generalized Chebyshev Polynomials
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 (hkTn−k)k and (hkU...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2018-06-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1278 |
| _version_ | 1827833363716636672 |
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| author | Abchiche Mourad Belbachir Hacéne |
| author_facet | Abchiche Mourad Belbachir Hacéne |
| author_sort | Abchiche Mourad |
| collection | DOAJ |
| description | 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 (hkTn−k)k and (hkUn−k)k, (0 ≤ k ≤ n − 1) are two bases of En(x) for which Tn and Un admit remarkable integer coordinates. |
| first_indexed | 2024-03-12T05:28:10Z |
| format | Article |
| id | doaj.art-eefc0378b14046439b96cf80fb17e824 |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T05:28:10Z |
| publishDate | 2018-06-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-eefc0378b14046439b96cf80fb17e8242023-09-03T07:11:41ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732018-06-01381799010.7151/dmgaa.1278dmgaa.1278Generalized Chebyshev PolynomialsAbchiche Mourad0Belbachir Hacéne1Faculty of Mathematics USTHB, RECITS Laboratory BP 32, El Alia, 16111 Bab Ezzouar, Algiers, AlgeriaFaculty of Mathematics USTHB, RECITS Laboratory BP 32, El Alia, 16111 Bab Ezzouar, Algiers, AlgeriaLet 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 (hkTn−k)k and (hkUn−k)k, (0 ≤ k ≤ n − 1) are two bases of En(x) for which Tn and Un admit remarkable integer coordinates.https://doi.org/10.7151/dmgaa.1278chebyshev polynomialsinteger coordinatespolynomial bases11b8315a0311b3908a40 |
| spellingShingle | Abchiche Mourad Belbachir Hacéne Generalized Chebyshev Polynomials Discussiones Mathematicae - General Algebra and Applications chebyshev polynomials integer coordinates polynomial bases 11b83 15a03 11b39 08a40 |
| title | Generalized Chebyshev Polynomials |
| title_full | Generalized Chebyshev Polynomials |
| title_fullStr | Generalized Chebyshev Polynomials |
| title_full_unstemmed | Generalized Chebyshev Polynomials |
| title_short | Generalized Chebyshev Polynomials |
| title_sort | generalized chebyshev polynomials |
| topic | chebyshev polynomials integer coordinates polynomial bases 11b83 15a03 11b39 08a40 |
| url | https://doi.org/10.7151/dmgaa.1278 |
| work_keys_str_mv | AT abchichemourad generalizedchebyshevpolynomials AT belbachirhacene generalizedchebyshevpolynomials |