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The purpose of this paper is to study the class of polynomial sets which are at the same time 𝑑-orthogonal and 𝑞-Appell. By a linear change of variable, the resulting set reduces to 𝑞-Al-Salam–Carlitz polynomials, for 𝑑 = 1. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order 𝑑 + 1. We also explicitly express a 𝑑-dimensional functional for which the d-orthogonality holds.
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2005
Keywords: Orthogonal polynomials; 𝑑-orthogonal polynomials; 𝑑-dimensional functional; 𝑞-difference operator
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