Zeros of Quasi-Orthogonal Jacobi Polynomials
We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α>−1, −2<β<−1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P(α,β)n and P(α,β+2)n are interla...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147743 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Zeros of Quasi-Orthogonal Jacobi Polynomials / K. Driver, K. Jordaan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ. |
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irk-123456789-1477432019-02-16T01:25:19Z Zeros of Quasi-Orthogonal Jacobi Polynomials Driver, K. Jordaan, K. We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α>−1, −2<β<−1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P(α,β)n and P(α,β+2)n are interlacing, holds when the parameters α and β are in the range α>−1 and −2<β<−1. We prove that the zeros of P(α,β)n and P(α,β)n₊₁ do not interlace for any n∈N, n≥2 and any fixed α, β with α>−1, −2<β<−1. The interlacing of zeros of P(α,β)n and P(α,β+t)m for m,n∈N is discussed for α and β in this range, t≥1, and new upper and lower bounds are derived for the zero of P(α,β)n that is less than −1. 2016 Article Zeros of Quasi-Orthogonal Jacobi Polynomials / K. Driver, K. Jordaan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C50; 42C05 DOI:10.3842/SIGMA.2016.042 http://dspace.nbuv.gov.ua/handle/123456789/147743 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α>−1, −2<β<−1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P(α,β)n and P(α,β+2)n are interlacing, holds when the parameters α and β are in the range α>−1 and −2<β<−1. We prove that the zeros of P(α,β)n and P(α,β)n₊₁ do not interlace for any n∈N, n≥2 and any fixed α, β with α>−1, −2<β<−1. The interlacing of zeros of P(α,β)n and P(α,β+t)m for m,n∈N is discussed for α and β in this range, t≥1, and new upper and lower bounds are derived for the zero of P(α,β)n that is less than −1. |
| format |
Article |
| author |
Driver, K. Jordaan, K. |
| spellingShingle |
Driver, K. Jordaan, K. Zeros of Quasi-Orthogonal Jacobi Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Driver, K. Jordaan, K. |
| author_sort |
Driver, K. |
| title |
Zeros of Quasi-Orthogonal Jacobi Polynomials |
| title_short |
Zeros of Quasi-Orthogonal Jacobi Polynomials |
| title_full |
Zeros of Quasi-Orthogonal Jacobi Polynomials |
| title_fullStr |
Zeros of Quasi-Orthogonal Jacobi Polynomials |
| title_full_unstemmed |
Zeros of Quasi-Orthogonal Jacobi Polynomials |
| title_sort |
zeros of quasi-orthogonal jacobi polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147743 |
| citation_txt |
Zeros of Quasi-Orthogonal Jacobi Polynomials / K. Driver, K. Jordaan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:12Z |
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2023-05-20T17:28:12Z |
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