Zeros of exceptional Hermite polynomials

DOI10.1016/j.jat.2015.07.002zbMath1331.33024arXiv1412.6364OpenAlexW1950077825MaRDI QIDQ498461

Robert Milson, Arno B. J. Kuijlaars

Publication date: 28 September 2015

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

Full work available at URL: https://arxiv.org/abs/1412.6364

zbMATH Keywords

zero distributionHermite polynomialsexceptional orthogonal polynomials

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 (22)

Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials ⋮ Recurrence relations for Wronskian Hermite polynomials ⋮ Determinantal formulas for exceptional orthogonal polynomials ⋮ The irreducibility of some Wronskian Hermite polynomials ⋮ Multiplication operator and average characteristic polynomial associated with exceptional Jacobi polynomials ⋮ A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ DEK-type orthogonal polynomials and a modification of the Christoffel formula ⋮ Convergence rates of exceptional zeros of exceptional orthogonal polynomials ⋮ Exceptional Gegenbauer polynomials via isospectral deformation ⋮ Exceptional Laurent biorthogonal polynomials through spectral transformations of generalized eigenvalue problems ⋮ General solution of the exceptional Hermite differential equation and its minimal surface representation ⋮ Asymptotic behavior of Wronskian polynomials that are factorized via \(p\)-cores and \(p\)-quotients ⋮ Exceptional Jacobi polynomials ⋮ Exceptional Orthogonal Polynomials and Rational Solutions to Painlevé Equations ⋮ Exceptional Legendre polynomials and confluent Darboux Transformations ⋮ The expansion of Wronskian Hermite polynomials in the Hermite basis ⋮ Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials ⋮ Asymptotics for recurrence coefficients of X₁-Jacobi exceptional polynomials and Christoffel function ⋮ Moments of random matrices and hypergeometric orthogonal polynomials ⋮ Spectral theory of exceptional Hermite polynomials ⋮ The electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation ⋮ On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A conjecture on exceptional orthogonal polynomials
• Zeros of the exceptional Laguerre and Jacobi polynomials
• Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger's equation
• Differential equations in the spectral parameter
• The spectral analysis of three families of exceptional Laguerre polynomials
• A modification of Crum's method
• Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials
• Zeros of Wronskians of Hermite polynomials and Young diagrams
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• The electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials and stable interpolation
• Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials
• Exceptional Charlier and Hermite orthogonal polynomials
• The zeros of linear combinations of orthogonal polynomials
• On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• ASSOCIATED STURM-LIOUVILLE SYSTEMS
• Monodromy-free Schrödinger operators with quadratically increasing potentials

This page was built for publication: Zeros of exceptional Hermite polynomials