A characterization of Hermite polynomials

DOI10.1016/S0377-0427(96)00144-6zbMath0881.33005OpenAlexW2038768045MaRDI QIDQ676152

Juan-Miguel Gracia

Publication date: 25 February 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(96)00144-6

zbMATH Keywords

Hermite polynomials

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (6)

Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions ⋮ Factorization of self-adjoint ordinary differential equations ⋮ Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ Self-adjoint differential equations for classical orthogonal polynomials ⋮ Generalized Hahn's theorem

Cites Work

• Die Charakterisierung der klassischen orthogonalen Polynome durch Sturm- Liouvillesche Differentialgleichungen
• On the classification of differential equations having orthogonal polynomial solutions
• Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
• Variations around classical orthogonal polynomials. Connected problems
• New characterizations of classical orthogonal polynomials
• Certain differential equations for Tchebycheff polynomials
• Characterizations of Orthogonal Polynomials Satisfying Differential Equations
• A New Class of Orthogonal Polynomials: The Bessel Polynomials

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