Математика Этерна
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On a different kind of d-orthogonal polynomials that generalize the Laguerre polynomials

Serhan Varma and Fatma Ta¸sdelen

The purpose of this work is to give an another generalization of the Laguerre polynomials in the context of d-orthogonality by a generating function of a certain form. We derive the d-dimensional functional vector for which the d-orthogonality holds. Some properties of the obtained polynomials are determined: expilicit representation, relation with a known polynomial, a recurrence relation of order-(d + 1) and a differential equation of order-(d + 1).