A Dunkl-classical d-symmetric d-orthogonal polynomial set

Abstract

In this paper, we apply a d-orthogonality preserving operator to the Humbert polynomials to derive a new Dunkl-classical d-orthogonal polynomials generalizing the Humbert ones. For the resulting polynomials, we state a (d+1)-order recurrence relation and a (d + 1)-order differential-difference equation. We also obtain an explicit expression of the d-dimensional functional vector for which the d-orthogonality holds. We show that the components of this d-symmetric Dunkl-classical d-orthogonal polynomial set are classical d-orthogonal.

Keywords

• d-orthogonal polynomials
• classical d-orthogonal polynomials
• dunkl-classical d-orthogonal polynomials
• d-symmetric polynomials
• components of a d-symmetric polynomial set
• humbert polynomials