Two-orthogonal polynomial sequences as eigenfunctions of a third-order differential operator

DOI10.1007/s00009-014-0511-1zbMath1346.42035OpenAlexW2126165512MaRDI QIDQ277017

Teresa Augusta Mesquita, Pascal Maroni

Publication date: 4 May 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-014-0511-1

zbMATH Keywords

linear functionalsAppell sequencesd-orthogonal polynomialslowering operators

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) Functional identities (associative rings and algebras) (16R60)

Related Items

On a new class of 2-orthogonal polynomials, I: the recurrence relations and some properties

Uses Software

• Mathematica

Cites Work

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• Two-dimensional orthogonal polynomials, their associated sets and the co- recursive sets
• Laplace transform inversion and Padé-type approximants
• On 2-orthogonal polynomials of Laguerre type
• Variations around classical orthogonal polynomials. Connected problems
• On \(d\)-orthogonal Tchebychev polynomials. I
• Some results on quasi-monomiality.
• Appell polynomial sequences with respect to some differential operators
• Connection problems via lowering operators
• Über die Jacobischen Polynome und zwei verwandte Polynomklassen
• Une caractérisation des polynômes \(d\)-orthogonaux classiques
• The relation of the \(d\)-orthogonal polynomials to the Appell polynomials
• Quadratic decomposition of Laguerre polynomials via lowering operators
• Quadratic decomposition of Appell sequences
• Constructing orthogonal matrix polynomials satisfying differential equations from two different Laguerre weights
• L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux
• LES POLYNÔMES ORTHOGONAUX „CLASSIQUES“ DE DIMENSION DEUX
• A generalized hypergeometric d -orthogonal polynomial set
• Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases
• On a polynomial sequence associated with the Bessel operator