In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, introduce new family quaternionic reproducing kernel Hilbert spaces the framework Fueter regular functions. The construction is based on general idea which allows us to obtain various function by specifying suitable sequence real numbers. We focus Fock and Hardy cases setting, a...

In this paper, binomial convolution in the frame of quantum calculus is studied for set Aq q-Appell sequences. It has been shown that sequences forms an Abelian group under operation convolution. Several properties structure have studied. A new definition polynomials associated with a random variable proposed. Scale transformation as well based on expectation respect to used present determinant...

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented. © 2007 Elsevier Inc. All rights reserved.

In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric f...