Asymptotic properties of orthogonal polynomials from their recurrence formula. I

DOI10.1016/0021-9045(85)90097-8zbMath0583.42011OpenAlexW4205941956MaRDI QIDQ1070156

Walter Van Assche

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-9045(85)90097-8

zbMATH Keywords

quadrature formulasrecurrence formula for orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (21)

Orthogonal polynomials with asymptotically periodic recurrent coefficients ⋮ Géza Freud, orthogonal polynomials and Christoffel functions. A case study ⋮ Eigenvalues of Toeplitz matrices associated with orthogonal polynomials ⋮ The ratio of q-like orthogonal polynomials ⋮ Asymptotic properties of orthogonal polynomials from their recurrence formula. II ⋮ A note on the zero distribution of orthogonal polynomials ⋮ On the extensions of some classical distributions ⋮ Ratio asymptotics for orthogonal matrix polynomials ⋮ On orthogonal polynomials obtained via polynomial mappings ⋮ Approximating the weight function for orthogonal polynomials on several intervals ⋮ The one-quarter class of orthogonal polynomials ⋮ Orthogonal polynomials, associated polynomials and functions of the second kind ⋮ Ratio asymptotics for orthogonal matrix polynomials with unbounded recurrence coefficients ⋮ Companion orthogonal polynomials: some applications ⋮ The distribution of the zeros of certain orthogonal polynomials ⋮ The strong Chebyshev distribution and orthogonal Laurent polynomials ⋮ Ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients ⋮ Inner products involving \(q\)-differences: The little \(q\)-Laguerre-Sobolev polynomials ⋮ Higher order hypergeometric Lauricella function and zero asymptotics of orthogonal polynomials ⋮ On some tridiagonal \(k\)-Toeplitz matrices: Algebraic and analytical aspects. applications ⋮ Relative asymptotics for orthogonal matrix polynomials with unbounded recurrence coefficients

Cites Work

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• On determining regular behavior from the recurrence formula for orthogonal polynomials
• Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues
• Remarks on E. A. Rahmanov's paper On the asymptotics of the ratio of orthogonal polynomials
• Orthogonal polynomials whose zeros are dense in intervals
• A class of orthogonal polynomials
• On Asymptotic Average Properties of Zeros of Orthogonal Polynomials
• Distribution of Zeros of Orthogonal Polynomials
• On the Regular Behaviour of Orthogonal Polynomials

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