Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials

DOI10.1016/S0377-0427(02)00645-3zbMath1017.33004OpenAlexW1978614574MaRDI QIDQ1874154

Dimitar K. Dimitrov

Publication date: 22 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(02)00645-3

zbMATH Keywords

monotonicityconvexityzerosLaguerre polynomialsultraspherical polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Real polynomials: location of zeros (26C10)

Related Items (4)

Zeros of Gegenbauer and Hermite polynomials and connection coefficients ⋮ Zeros of pseudo-ultraspherical polynomials ⋮ Convexity results for the largest zero and functions involving the largest zero ofq-associated polynomials ⋮ Asymptotic behaviour of Jacobi polynomials and their zeros

Cites Work

• On the behaviour of zeros of Jacobi polynomials
• On the variation with respect to a parameter of zeros of Bessel and q- Bessel functions
• Monotonicity properties of the zeros of ultraspherical polynomials
• On a conjecture concerning monotonocity of zeros of ultraspherical polynomials
• On eigenvalues of matrices dependent on a parameter
• On the Square of the Zeros of Bessel Functions
• Matrix Analysis
• Inequalities and Numerical Bounds for Zeros of Ultraspherical Polynomials
• A theorem concerning differentiability of eigenvectors and eigenvales with some applications
• A Monotonic Property for the Zeros of Ultraspherical Polynomials
• Concavity and convexity of eigenvalues
• Asymptotic Formulas for Ultraspherical Polynomials P (λ) n (X) and their Zeros for Large Values of λ
• On the Square of the First Zero of the Bessel Function J_v(z)
• On the Derivative with Respect to a Parameter of a Zero of a Sturm–Liouville Function
• Convexity of the largest zero of the ultraspherical polynomials
• A Discrete Approach to Monotonicity of Zeros of Orthogonal Polynomials
• Some recent results on the zeros of Bessel functions and orthogonal polynomials
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