On the constant coefficients of a certain recurrence relation: A simple proof
In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-08-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844021018673 |
| _version_ | 1831788667306246144 |
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| author | Milica Anđelić Carlos M. da Fonseca |
| author_facet | Milica Anđelić Carlos M. da Fonseca |
| author_sort | Milica Anđelić |
| collection | DOAJ |
| description | In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families. |
| first_indexed | 2024-12-22T13:52:40Z |
| format | Article |
| id | doaj.art-0e7c7b30675c4f92b2c87fb5d5d7a595 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-22T13:52:40Z |
| publishDate | 2021-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-0e7c7b30675c4f92b2c87fb5d5d7a5952022-12-21T18:23:37ZengElsevierHeliyon2405-84402021-08-0178e07764On the constant coefficients of a certain recurrence relation: A simple proofMilica Anđelić0Carlos M. da Fonseca1Department of Mathematics, Kuwait University, Safat 13060, KuwaitKuwait College of Science and Technology, Doha District, Safat 13133, Kuwait; Chair of Computational Mathematics, University of Deusto, 48007 Bilbao, Basque Country, Spain; Corresponding author at: Kuwait College of Science and Technology, Doha District, Safat 13133, Kuwait.In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.http://www.sciencedirect.com/science/article/pii/S2405844021018673Recurrence relationDeterminantTridiagonal k-Toeplitz matricesChebyshev polynomials of second kind |
| spellingShingle | Milica Anđelić Carlos M. da Fonseca On the constant coefficients of a certain recurrence relation: A simple proof Heliyon Recurrence relation Determinant Tridiagonal k-Toeplitz matrices Chebyshev polynomials of second kind |
| title | On the constant coefficients of a certain recurrence relation: A simple proof |
| title_full | On the constant coefficients of a certain recurrence relation: A simple proof |
| title_fullStr | On the constant coefficients of a certain recurrence relation: A simple proof |
| title_full_unstemmed | On the constant coefficients of a certain recurrence relation: A simple proof |
| title_short | On the constant coefficients of a certain recurrence relation: A simple proof |
| title_sort | on the constant coefficients of a certain recurrence relation a simple proof |
| topic | Recurrence relation Determinant Tridiagonal k-Toeplitz matrices Chebyshev polynomials of second kind |
| url | http://www.sciencedirect.com/science/article/pii/S2405844021018673 |
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