Zeros of Jacobi and ultraspherical polynomials

DOI10.1007/s11139-021-00480-1arXiv2009.10196OpenAlexW3201977192MaRDI QIDQ6098231

Lance L. Littlejohn, Jorge Arvesú, Kathy A. Driver

Publication date: 13 June 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.10196

zbMATH Keywords

zerosJacobi polynomialsthree-term recurrence relationinterlacing

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10)

Cites Work

• Unnamed Item
• Bounds for extreme zeros of some classical orthogonal polynomials
• Interlacing of zeros of orthogonal polynomials under modification of the measure
• Interlacing of the zeros of Jacobi polynomials with different parameters
• Quasi-orthogonality with applications to some families of classical orthogonal polynomials.
• Zeros of Jacobi polynomials \(P_{n}^{(\alpha ,\beta)} \), \(- 2 < \alpha\), \(\beta < -1\)
• Stieltjes interlacing of zeros of Jacobi polynomials from different sequences
• Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials
• Interlacing of zeros of Laguerre polynomials of equal and consecutive degree

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