\(d\)-orthogonality via generating functions

DOI10.1016/j.cam.2005.01.051zbMath1119.42009OpenAlexW2004645845MaRDI QIDQ849600

Youssèf Ben Cheikh, Ali Zaghouani

Publication date: 31 October 2006

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.01.051

zbMATH Keywords

integral representationslinear functionalsSheffer polynomialshypergeometric polynomialslowering operators\(d\)-orthogonal polynomialsBrenke polynomialstransform 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) Other special orthogonal polynomials and functions (33C47) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (28)

Operational rules and d-orthogonal polynomials of Laguerre type ⋮ \(d\)-orthogonality and \(q\)-Askey-scheme ⋮ L-classical d-orthogonal polynomial sets of Sheffer type ⋮ Generating functions via integral transforms ⋮ \(d\)-orthogonality of discrete \(q\)-Hermite type polynomials ⋮ \(d\)-orthogonality of a generalization of both Laguerre and Hermite polynomials ⋮ Some generalized hypergeometric \(d\)-orthogonal polynomial sets ⋮ On \(d\)-orthogonal polynomials with Brenke type generating functions ⋮ Operational rules for a new family of d -orthogonal polynomials of Laguerre type ⋮ A characterization of Dunkl-classical \(d\)-symmetric \(d\)-orthogonal polynomials and its applications ⋮ \(d\)-orthogonality of little \(q\)-Laguerre type polynomials ⋮ On \(d\)-symmetric classical \(d\)-orthogonal polynomials ⋮ On the zeros of \(d\)-symmetric \(d\)-orthogonal polynomials ⋮ Some Characterization Problems Related to Sheffer Polynomial Sets ⋮ On semi‐classical d‐orthogonal polynomials ⋮ \(d\)-Orthogonality of Hermite type polynomials ⋮ Limit relations involving 2-orthogonal polynomials ⋮ Ond-orthogonal polynomials of Sheffer type ⋮ \(d\)-orthogonality of Humbert and Jacobi type polynomials ⋮ Dunkl–Appelld-orthogonal polynomials ⋮ Asymptotic relations involving \(d\)-orthogonal polynomials ⋮ On Mittag-Leffler \(d\)-orthogonal polynomials ⋮ On connection sequence for equivalent polynomial sets ⋮ On some operators varying the dimensional parameters of d-orthogonality ⋮ Automorphisms of the q-deformed algebra su_q(1, 1) and d-Orthogonal polynomials of q-Meixner type ⋮ Hahn-Appell polynomials and their \(d\)-orthogonality ⋮ On Askey-scheme and \(d\)-orthogonality. I: A characterization theorem ⋮ Some new d-orthogonal polynomial sets of Sheffer type

Cites Work

• Vector orthogonal relations. Vector QD-algorithm
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• Some results on quasi-monomiality.
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• Multiple orthogonal polynomials for classical weights
• A generalized hypergeometric d -orthogonal polynomial set
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