Zeros of Quasi-Orthogonal Jacobi Polynomials
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Zeros of Quasi-Orthogonal Jacobi Polynomials
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| Creator |
Driver, K.
Jordaan, K. |
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| 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.
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| Date |
2019-02-15T19:02:14Z
2019-02-15T19:02:14Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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