Difference equations of q-Appell polynomials

$\psi$-Appell polynomials` solutions of an umbral difference nonhomogeneous equation

One discovers why Morgan Ward solution [1] of ψ-difference calculus nonhomogeneous equation ∆ ψ f = ϕ in the form f (x) = n≥1 B n n ψ ! ϕ (n−1) (x) + ψ ϕ(x) + p(x) recently proposed by the present author (see-below)-extends here now to ψ-Appell polynomials case-almost automatically. The reason for that is just proper framework i.e. that of the ψ-Extended Finite Operator Calculus(EFOC) recently ...

Analytic q-difference equations

A complex number q with 0 < |q| < 1 is fixed. By an analytic q-difference equation we mean an equation which can be represented by a matrix equation Y (z) = A(z)Y (qz) where A(z) is an invertible n× n-matrix with coefficients in the field K = C({z}) of the convergent Laurent series and where Y (z) is a vector of size n. The aim of this paper is to give an overview of our present knowledge of th...

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.

q-Hypergeometric solutions of q-difference equations

We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...

M ay 2 00 4 ψ - Appell polynomials ’ solutions of the Q ( ∂ ψ ) - difference calculus nonhomogeneous equation