Abstract
More than one hundred years ago, Appell introduced a polynomials class characterized by the exponential form of its generator function. This class is well-known on R and the aim of this paper is to offer a multi-dimensional analysis in two directions: we indicate a classical characterization of the Appell polynomials on R d via their generator function and we investigate their orthogonality. Two types of orthogonality are characterized. We relate this study to the theory of Lie algebras and martingales.
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