In this paper, we give two characterization theorems to introduce new examples of basic hypergeometric d -orthogonal polynomials which, on the one hand, generalize the known q-Meixner, big q-Laguerre, little q-Laguerre and q-Laguerre polynomials and, on the other hand, can be viewed as q-analogs of d -orthogonal polynomials of Meixner and Laguerre type. For the resulting polynomials, we state some properties.
In this paper, we treat three questions related to the d-orthogonality of the Humbert polynomials. The first one consists to determinate the explicit expression of the d-dimensional functional vector for which the d-orthogonality holds. The second one is the investigation of the components of Humbert polynomial sequence. That allows us to introduce, as far as we know, new d-orthogonal polynomials generalizing the classical Jacobi ones. The third one consists to solve a characterization problem related to a generalized hypergeometric representation of the Humbert polynomials.
In this paper, we use some integral transforms to derive, for a polynomial sequence {P n (x)} n 0 , generating functions of the type G γ (x, t) = ∞ n=0 γ n P n (x)t n , starting from a generating function of type G(x, t) = ∞ n=0 P n (x)t n , where {γ n } n 0 is a real numbers sequence independent on x and t. That allows us to unify the treatment of a generating function problem for many well-known polynomial sequences in the literature.
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