Monotonicity properties of the zeros of ultraspherical polynomials

DOI10.1006/jath.1996.3259zbMath0923.33004OpenAlexW2002764591MaRDI QIDQ1288261

Panayiotis D. Siafarikas, Árpád Elbert

Publication date: 28 October 1999

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1996.3259

zbMATH Keywords

ultraspherical polynomial

Mathematics Subject Classification ID

Spherical harmonics (33C55)

Related Items (17)

A connection between ultraspherical and pseudo-ultraspherical polynomials ⋮ Árpád Elbert, 1939--2001: A memorial tribute. ⋮ Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials ⋮ Some monotonicity results on the zeros of the generalized Laguerre polynomials ⋮ Zeros of Gegenbauer and Hermite polynomials and connection coefficients ⋮ Zeros of pseudo-ultraspherical polynomials ⋮ Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems ⋮ Zeros of a family of hypergeometric para‐orthogonal polynomials on the unit circle ⋮ A survey on Markov's theorem on zeros of orthogonal polynomials ⋮ Monotonicity of zeros of Jacobi polynomials ⋮ Monotonicity of zeros of polynomials orthogonal with respect to an even weight function ⋮ On the behaviour of zeros of Jacobi polynomials ⋮ On Markov's theorem on zeros of orthogonal polynomials revisited ⋮ Differential inequalities of functions involving the lowest zero of some associated orthogonalq-polynomials ⋮ Some recent results on the zeros of Bessel functions and orthogonal polynomials ⋮ Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications, Rome, Italy, June 18--22, 2001. Dedicated to the memory of Professor Árpád Elbert ⋮ Monotonicity of zeros of Laguerre polynomials

Cites Work

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• Upper bounds for the zeros of ultraspherical polynomials
• On a conjecture concerning monotonocity of zeros of ultraspherical polynomials
• A Note to the Paper of Ahmed, Muldoon and Spigler
• Inequalities and Numerical Bounds for Zeros of Ultraspherical Polynomials
• A Monotonic Property for the Zeros of Ultraspherical Polynomials
• Asymptotic Formulas for Ultraspherical Polynomials P (λ) n (X) and their Zeros for Large Values of λ
• On the Derivative with Respect to a Parameter of a Zero of a Sturm–Liouville Function

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