The convolution transform and Appell polynomials

Appell Polynomials and Their Relatives

This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...

On Multiple Appell Polynomials

In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.

Turan’s Inequality for Appell Polynomials

Matrix approach to Appell polynomials

In the last years the Appell polynomials, named after Paul Émile Appell which introduced them in 1880 [1], have gained renewed interest and has been studied by several authors. In particular, some new characterizations of Appell polynomials themselves through new approaches have been considered. To quote some of them we mention, for instance, the novel approach developed in [5], which makes use...

Generalizations of the Bernoulli and Appell Polynomials

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper)...