Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

DOI10.1007/S11075-013-9807-7zbMath1306.33020OpenAlexW2074986700WikidataQ122889306 ScholiaQ122889306MaRDI QIDQ483278

Fernando Rodrigo Rafaeli, Yen Chi Lun

Publication date: 16 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-013-9807-7

zbMATH Keywords

inequalitieszerosJacobi polynomialsSturm's theoremGautschi's conjectures

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (1)

Monotonicity of zeros for a class of polynomials including hypergeometric polynomials

Uses Software

• CIZJP

Cites Work

• Unnamed Item
• Bounds for extreme zeros of some classical orthogonal polynomials
• On conjectured inequalities for zeros of Jacobi polynomials
• New conjectured inequalities for zeros of Jacobi polynomials
• On a conjectured inequality for the largest zero of Jacobi polynomials
• Conjectured inequalities for Jacobi polynomials and their largest zeros
• Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials
• Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
• On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials
• On the Spacing of the Zeros of Some Classical Orthogonal Polynomials
• Worst-case errors in a Sobolev space setting for cubature over the sphere S²
• Zeros of a family of hypergeometric para‐orthogonal polynomials on the unit circle

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