Estimates of the orthogonal polynomials with weight \(\exp (-x^ m)\), m an even positive integer

DOI10.1016/0021-9045(86)90074-2zbMath0619.33007OpenAlexW2013180156MaRDI QIDQ1089480

Stanford S. Bonan, Dean S. Clark

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0021-9045(86)90074-2

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (16)

The recurrence coefficients of the orthogonal polynomials with the weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$ ⋮ Géza Freud, orthogonal polynomials and Christoffel functions. A case study ⋮ On Freud's equations for exponential weights ⋮ Mean convergence of Lagrange interpolation for Freud's weights with application to product integration rules ⋮ Pointwise convergence of Lagrange interpolation based at the zeros of orthonormal polynomials with respect to weights on the whole real line ⋮ Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials ⋮ A degenerate Gaussian weight connected with Painlevé equations and Heun equations ⋮ The recurrence coefficients of a semi-classical Laguerre polynomials and the large n asymptotics of the associated Hankel determinant ⋮ A singular linear statistic for a perturbed LUE and the Hankel matrices ⋮ Mehler–Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight ⋮ Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I. ⋮ Estimates of the Hermite and the Freud polynomials ⋮ Estimates of asymmetric Freud polynomials on the real line ⋮ Novel Universal Correlations in Invariant Random-Matrix Models ⋮ Singular linear statistics of the Laguerre unitary ensemble and Painlevé. III. Double scaling analysis ⋮ Pointwise asymptotics of the ratio of Jacobi-type polynomials

Cites Work

• Exact bounds for orthogonal polynomials associated with exponential weights
• On Nevai's bound for orthogonal polynomials associated with exponential weights
• Mean convergence of Lagrange interpolation for Freud's weights with application to product integration rules
• Asymptotic Expansions of Ratios of Coefficients of Orthogonal Polynomials with Exponential Weights
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