On semi‐classical  d ‐orthogonal polynomials | Zendy

Saib Abdessadek | Zendy

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On semi‐classical d ‐orthogonal polynomials

Author(s) -

Saib Abdessadek

Publication year - 2013

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201200176

Subject(s) - mathematics , orthogonal polynomials , orthogonality , classical orthogonal polynomials , discrete orthogonal polynomials , sequence (biology) , pure mathematics , wilson polynomials , jacobi polynomials , hahn polynomials , type (biology) , gegenbauer polynomials , property (philosophy) , algebra over a field , geometry , ecology , philosophy , epistemology , biology , genetics

In this paper a general theory of semi‐classical d ‐orthogonal polynomials is developed. We define the semi‐classical linear functionals by means of a distributional equation( Φ U ) ′ = Ψ U , where Φ and Ψ are d × d matrix polynomials. Several characterizations for these semi‐classical functionals are given in terms of the corresponding d ‐orthogonal polynomials sequence. They involve a quasi‐orthogonality property for their derivatives and some finite‐type relations.

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