Characterization of Laguerre polynomials as orthogonal polynomials connected by the Laguerre degree raising shift operator

DOI10.1007/s11139-017-9901-xzbMath1381.33012OpenAlexW2610956764MaRDI QIDQ682014

Baghdadi Aloui

Publication date: 13 February 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-017-9901-x

zbMATH Keywords

orthogonal polynomialsLaguerre polynomialslinear functionalsclassical polynomialsLaguerre degree raising shift operator

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 (7)

BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS ⋮ Some new connection relations related to classical orthogonal polynomials ⋮ Classical orthogonal polynomials via a second-order linear differential operators ⋮ Jacobi polynomials and some connection formulas in terms of the action of linear differential operators ⋮ Connection formulas and representations of Laguerre polynomials in terms of the action of linear differential operators ⋮ Unnamed Item ⋮ HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)

Cites Work

• Über Polynomsysteme, die Sturm-Liouvilleschen Differenzengleichungen genügen
• Divided difference operators and classical orthogonal polynomials
• The \(D_ \omega\)-classical orthogonal polynomials
• The \(H_q\)-classical orthogonal polynomials
• Classical orthogonal polynomials with respect to a lowering operator generalizing the Laguerre operator
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
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