Certain Properties and Characterizations of Multivariable Hermite-Based Appell Polynomials via Factorization Method

Characterizations of Generalized Hermite and Sieved Ultraspherical Polynomials

A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the measure |x|γ(1 − x2)1/2dx is derived which is based on a “reversing property” of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalizati...

Multivariable Appell Functions

Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain s`(m, 1)∧ modules. Recently Bringmann and Ono showed that the character formulas for the s`(m, 1)∧ modules L(Λ(s)), where L(Λ(s)) is the irreducible s`(m, 1) ∧ module with highest weight Λ(s), can be seen as the “holomorphic parts” of certain nonholomorphic modular functio...

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.

Miscellaneous properties of some multivariable polynomials