We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an appr...

Inspired by the work of Schur on Taylor series exponential and Laguerre polynomials, we study Galois theory trimmed exponentials $f_{n,n+k}=\sum _{i=0}^{k} {x^{i}/(n+i)!}$ generalized polynomials $L^{(n)}_k$ degree

In this paper, we obtain the extended Wright generalized Hypergeometric function using extended Beta function. We also obtain certain integral representations, Mellin transform and some derivative properties of extended Wright generalized Hypergeometric function. Further, we represent extended Wright generalized Hypergeometric function in the form of Laguerre polynomials and Whittaker function.

Abstract We extend to matrix-valued stochastic processes, some well-known relations between realvalued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and martingale polynomials. In particular, joint semigroup densities of the eigenvalue processes of the generalized matrix-valued Ornstein-Uhlenbeck and squared OrnsteinUhlenbeck processes are ...

We introduce the so-called Clifford–Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related ...

Abstract. In recent years classical polynomials of a real or complex variable and their generalizations to the case of several real or complex variables have been in a focus of increasing attention leading to new and interesting problems. In this paper we construct higher dimensional analogues to generalized Laguerre and Hermite polynomials as well as some based functions in the framework of Cl...