On the complex zeros of some families of orthogonal polynomials

DOI10.1155/2010/263860zbMath1200.30002OpenAlexW2100709563WikidataQ58649803 ScholiaQ58649803MaRDI QIDQ1957565

Eugenia N. Petropoulou

Publication date: 27 September 2010

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/229868

zbMATH Keywords

Jacobi polynomialsLaguerre polynomials

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Cites Work

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• Limit relations for the complex zeros of Laguerre and \(q\)-Laguerre polynomials
• Self-adjoint difference operators and symmetric Al-Salam-Chihara polynomials
• On the zeros of a class of polynomials including the generalized Bessel polynomials
• Newton sum rules and monotonicity properties of the zeros of scaled co-recursive associated polynomials
• The moment problem associated with the \(q\)-Laguerre polynomials
• Electrostatics and the Zeros of the Classical Polynomials
• Recurrence relations for radial wavefunctions for theNth-dimensional oscillators and hydrogenlike atoms
• Convexity results for the largest zero and functions involving the largest zero ofq-associated polynomials
• Differential inequalities of functions involving the lowest zero of some associated orthogonalq-polynomials
• Convexity of the largest zero of the ultraspherical polynomials
• Zeros of the hypergeometric polynomials \(F(-n,b;2b;z)\)
• Zeros of ultraspherical polynomials and the Hilbert-Klein formulas
• Generalized \(q\)-Hermite polynomials

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