Operational rules for a new family of d-orthogonal polynomials of Laguerre type

The aim of this research is to present a new generalization of d-orthogonal $ (d\geq 2) $ ( d ≥ 2 ) polynomials of Laguerre type by utilizing a suitable generating function from Sheffer class and employing operational rules associated with the lowering and raising operators that satisfy d-orthogonal...

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Bibliographic Details
Published inIntegral transforms and special functions Vol. 35; no. 2; pp. 77 - 94
Main Authors Benamira, Wissem, Nasri, Ahmed, Ellaggoune, Fateh
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.02.2024
Taylor & Francis Ltd
Subjects
connection coefficients
d-orthogonal polynomials of Laguerre type
d-orthogonality
generating function
lowering operator
Polynomials
quasi-monomiality principle
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Summary:The aim of this research is to present a new generalization of d-orthogonal $ (d\geq 2) $ ( d ≥ 2 ) polynomials of Laguerre type by utilizing a suitable generating function from Sheffer class and employing operational rules associated with the lowering and raising operators that satisfy d-orthogonality. We derive several properties of these polynomials and establish the recurrence relation. Moreover, we provide explicit, connection and inversion formulas, the $ ( d+1) $ ( d + 1 ) -order differential equation, and the canonical d-dimensional functional vector.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2023.2272758