Zeros of the exceptional Laguerre and Jacobi polynomials

DOI10.5402/2012/920475zbMath1252.33008arXiv1102.5669OpenAlexW2171096540WikidataQ58905370 ScholiaQ58905370MaRDI QIDQ454504

Ryu Sasaki, Choon-Lin Ho

Publication date: 8 October 2012

Published in: ISRN Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5669

zbMATH Keywords

classical orthogonal polynomialsHamiltonians changepositive-definite measure

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 (19)

Group theoretic approach to rationally extended shape invariant potentials ⋮ On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials ⋮ Supersymmetry and shape invariance of exceptional orthogonal polynomials ⋮ Extensions of a class of similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries ⋮ A class of exactly solvable rationally extended non-central potentials in two and three dimensions ⋮ A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems ⋮ A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ Convergence rates of exceptional zeros of exceptional orthogonal polynomials ⋮ Exceptional Laurent biorthogonal polynomials through spectral transformations of generalized eigenvalue problems ⋮ Rationally extended many-body truncated Calogero-Sutherland model ⋮ The spectral analysis of three families of exceptional Laguerre polynomials ⋮ General solution of the exceptional Hermite differential equation and its minimal surface representation ⋮ Exceptional Jacobi polynomials ⋮ Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials ⋮ Zeros of exceptional Hermite polynomials ⋮ Recurrence relations of the multi-indexed orthogonal polynomials ⋮ Extended Krein-Adler theorem for the translationally shape invariant potentials ⋮ Moment representations of exceptional \(X_{1}\) orthogonal polynomials ⋮ One parameter family of rationally extended isospectral potentials

Cites Work

• Properties of the exceptional \((X_{l})\) Laguerre and Jacobi polynomials
• Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
• Solvable rational extensions of the isotonic oscillator
• Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics
• An extension of Bochner's problem: exceptional invariant subspaces
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Solvable rational extensions of the Morse and Kepler-Coulomb potentials
• Solvable rational extension of translationally shape invariant potentials
• Exceptional orthogonal polynomials and the Darboux transformation
• The Exceptional (X ) (q)-Racah Polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations
• Conditionally exactly solvable potentials and exceptional orthogonal polynomials
• Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
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