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

AbstractThe aim of this research is to present a new generalization of d-orthogonal (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)-order differential equation, and the canonical d-dimensional functional vector.Keywords: d-orthogonalityd-orthogonal polynomials of Laguerre typegenerating functionlowering operatorquasi-monomiality principleconnection coefficientsAMS Classifications: 33C4539A7041A5842C05 AcknowledgmentsThe authors thank the referees for their careful reading of the manuscript and for their constructive comments and suggestions.Data availability statementData sharing not applicable to this article as no data sets were generated or analyzed during the current study.Disclosure statementNo potential conflict of interest was reported by the author(s).