Characterization of q-Dunkl Appell symmetric orthogonal q-polynomials

Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions

“…t n γ n (2.5) (in addition to the papers [1,21] cited in the introduction, Appell-Dunkl sequences have been considered also, for instance, in [4,6,12]). From this definition, it is not difficult to prove that A n (x) is a polynomial of degree n and Λ α A n (x) = γn γn−1 A n−1 (x) (when α = −1/2, this becomes the classical A ′ n (x) = nA n−1 (x) of Appell sequences).…”

“…(in addition to the papers [1,21] cited in the introduction, Appell-Dunkl sequences have been considered also, for instance, in [4,6,12]). From this definition, it is not difficult to prove that A n (x) is a polynomial of degree n and Λ…”