Prof. Paul Appell

Prof. Dr. Prof. Prof.

Appell hypergeometric partial differential equations

Mathematicians often speak of the unity of their subject. Such a unity from the 19th century origins in the history of linear ordinary differential equations, especially those closely connected with elliptic and modular functions. It is concerned with the impact of group theoretical and geometrical ideas upon the problem of understanding the nature of the solutions to a differential equation (s...

Generalized Appell Systems

We give a general approach to in nite dimensional non-Gaussian analysis which generalizes the work [KSWY95]. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.

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