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

Abstract

The aim of this research is to present a new generalization of d-orthogonal 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 -order differential equation, and the canonical d-dimensional functional vector.