Formula omitted]-orthogonality of Little [formula omitted]-Laguerre type polynomials

Abstract

In this paper, we solve a characterization problem in the context of the d -orthogonality. That allows us, on one hand, to provide a q -analog for the d -orthogonal polynomials of Laguerre type introduced by the first author and Douak, and on the other hand, to derive new L q -classical d -orthogonal polynomials generalizing the Little q -Laguerre polynomials. Various properties of the resulting basic hypergeometric polynomials are singled out. For d = 1 , we obtain a characterization theorem involving, as far as we know, new L q -classical orthogonal polynomials, for which we give the recurrence relation and the difference equation.